With brief exceptions, the Medici ruled Florence from the mid-15th until the mid-18th century, rising from the lowly rank of traders in textiles to become bankers, warlords and grand dukes.

When one branch of the family withered, cousins stepped in to perpetuate the Medicis’ pursuit of power. Theirs was a constant quest for legitimation, by force of arms, through political office and marriage to nobility.

The Medici produced four popes and two queens of France. But they are best remembered for their patronage of the arts and science. Medici proteges included the geniuses of the Florentine Renaissance, including Masaccio, Brunelleschi, Donatello, Fra Angelico, Michelangelo, Leonardo, and Galileo.

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The power of the Medici culminated in the late Renaissance, with Cosimo I the Great, who ruled Tuscany from 1537 until his death in 1574.

The 16th century opened unpropitiously for the Medici, when they were expelled from Florence by the mad monk Girolamo Savonarola. Although Savonarola's reign of terror lasted only four years, he ushered in decades of austerity in the arts.

The Medici took advantage of the endless war between the Holy Roman Emperor and the pope to plot their own return.

Events transformed the art of the portrait, as shown by the exhibition Florence: Portraits at the Court of the Medicis in Paris. The painters on exhibit include Del Sarto, Pontormo, Salviati and especially Bronzino, the favourite painter at the court of the Medici. Inspired by Leonardo and Raphael, these painters broke with classical rules to explore what the art historian Giorgio Vasari called "the modern manner", a more complex, sophisticated and original way of painting. They later became known as mannerists.

"We concentrated on the 16th century because, until then, the portrait was a minor, unappreciated genre," says Nicolas Sainte Fare Garnot, the curator of Jacquemart-André and co-commissioner of the exhibition. "The Medici needed images, particularly portraits, to establish their power. They used portraits as a propaganda weapon. That's the story behind this exhibition."

Violent times

The rule of the Medici was interrupted twice, from the death of Lorenzo the Magnificent in 1492 until 1513, and again from 1527 until 1530. These were violent times. In 1527, the emperor’s mutinous troops murdered up to 12,000 people in Rome and pillaged the city for eight months. The proliferation of dead bodies led to an outbreak of plague.

“The imperial armies burned Rome,” notes Sainte Fare Garnot. “Some considered the emperor to be the anti-Christ. They thought it was the apocalypse, that if the holy city could be destroyed, it was proof the world was ending.”

There are no Medicis in the first room of the exhibition, where one is immediately drawn to the portrait of Savonarola, painted in 1498, the year the monk was arrested, tortured, hanged and burned, his ashes scattered in the Arno River. Fra' Bartolomeo painted the monk, who believed he had been sent by God to burn Bocaccio's books and Botticelli's paintings on his Bonfire of the Vanities.

Towards the end of the 15th century, portraitists stopped painting subjects in profile, favouring instead the three-quarter view, to better reveal the sitter's character. With his black cowl, prominent nose and mad stare, Fra' Bartolomeo's Savonarola is a throwback to the previous period.

Despite Savonarola's demise, his abhorrence of wealth, luxury and sensual pleasures persisted for 2½ decades. Women covered their hair, as in Ridolfo del Ghirlandaio's Portrait of a Veiled Woman, because female hair was considered erotically provocative. Sitters of the early 16th century wore black, like the men in Jacopo Pontormo's unusual Double Portrait. In an early example of mannerism, Pontormo made it impossible to tell which man of what appears to be a homosexual couple holds the page from Cicero's Treatise on Friendship.

Vasari was the ultimate Renaissance man: decorator, painter, author of the Lives of the Artists. In 1534 he painted Alessandro de Medici, the first duke of Florence, in a suit of armour, contemplating the city that he conquered through a brutal year-long siege. The three-legged stool Alessandro is perched on signified perpetual rule, the red cloth the blood bath he perpetrated to attain it, Vasari wrote.

Alessandro was murdered in bed by his cousin Lorenzaccio, and replaced by another cousin, Cosimo I. Under Cosimo’s long reign, portraiture would flourish as never before. “It needed the stability of a dynasty for the art form to establish itself and develop over such a long period,” Sainte Fare Garnot explains.

The era was still one of military conquest. To convey the message that the Medici held power by force of arms, Bronzino painted Cosimo in armour.

“Cosimo had at least 30 copies painted, to hang in public places and in embassies abroad, to show that he was in charge,” says Sainte Fare Garnot. “Today, the portrait of the French president hangs in every town hall in France. Sixteenth- century Florence is where the tradition started.”

As the Medici consolidated power, they stopped representing themselves as condottiere. A later portrait of Cosimo, also by Bronzino, shows him dressed in mink and purple silk. In 1539, Cosimo sealed his alliance with Spain and the Holy Roman Empire by marrying Eleanor of Toledo, the daughter of the Spanish viceroy of Naples. Eleanor's blue blood paved the way for Cosimo's ascension to the title of grand duke.

Bronzino’s magnificent 1543 portrait of Eleanor, on loan from the National Gallery of Prague, is the signature portrait of the exhibition. Against a background painted with lapis lazuli, the grand duchess poses in pink satin embroidered with gold thread and pearls; luxury that would have made Savonarola apoplectic.

The courtesans surrounding the Medici wanted to have their portraits painted too, to demonstrate their status, and for posterity. Once the craze for portraits in armour ended, elegant women became preferred models. Lower-ranking aristocracy struck more relaxed poses, like Bronzino's Portrait of a Lady in Red. She holds a small dog, and, true to mannerist tradition, seems to twist on her chair.

Cosimo I founded the Florentine Academy of Letters and, with his advisor Vasari, the Academy of Fine Arts. In an age that revered literature and music, affluent courtesans were eager to demonstrate their own learning. Painters had long been considered little better than manual workers, and they wanted to place themselves on a level with poets.

Musical instrument

The result was a fad for portraits in which the sitter holds either a book by one of Florence's founding poets – Dante, Petrarch or Boccaccio – or a musical instrument, usually a lute, considered aristocratic. The Jacquemart-André museum is showing one of its treasures in the exhibition, The Lute Player, by Francesco Salviati.

Salviati, a Florentine painter called Francesco de’ Rossi, went to Rome where he adopted the name of his patron, Cardinal Salviati. The lute player has been identified as the French musician Jacquet du Pont. He is playing a G major chord, one of the most difficult.

Mannerist painters usually avoided primary colours. The Lute Player is an unusual harmony of green, yellow, brown and orange. The striped fabric in front of the musician suggests a keyboard; the irregular bands the rhythm and sonority of music.

By the end of the 16th century, head-and-shoulders portraits had graduated to full-length effigies, such as Santi di Tito’s portrait of Marie de’ Medici, granddaughter of Eleanor of Toledo and Cosimo I. The painting celebrates Marie’s marriage in 1600 to King Henri IV of France. She wears a lace ruff and sumptuous robes embroidered with the fleur de lys, symbol of French royalty. The visitor has only to retrace his or her steps back to the austere portraits of Savonarola and his contemporaries to see how great a distance the Florentine portrait travelled in one century.

• Florence: Portraits at the Court of the Medicis is at the Musée Jacquemart-André in Paris until January 25th, 2016

MEDICI MADNESS: A TIMELINE

1434 The Medici become Florence's leading family, under Cosimo the Elder

1492 Lorenzo the Magnificent dies and is replaced by his bedridden son "Piero the Gouty"

1494-1498 The Medici are exiled. Theocracy under Girolamo Savonarola ends with the monk's execution

1513-1527 Return of the Medici, who are expelled a second time

1530-1537 Alessandro de' Medici lays siege to Florence, rules as duke and is murdered by his cousin, Lorenzaccio

1537-1574 Reign of Cosimo I, "the builder". Married to Eleanor of Toledo, Cosimo obtains the title of Grand Duke in 1569 1743 The Grand Ducal line ends with the death of Anna Maria Luisa de' Medici

1434 The Medici become Florence's leading family, under Cosimo the Elder

1492 Lorenzo the Magnificent dies and is replaced by his bedridden son "Piero the Gouty"

1494-1498 The Medici are exiled. Theocracy under Girolamo Savonarola ends with the monk's execution

1513-1527 Return of the Medici, who are expelled a second time

1530-1537 Alessandro de' Medici lays siege to Florence, rules as duke and is murdered by his cousin Lorenzaccio

1537-1574 Reign of Cosimo I, "the builder". Married to Eleanor of Toledo, Cosimo obtains the title of Grand Duke in 1569 1743 The Grand Ducal line ends with the death of Anna Maria Luisa de' Medici