A splendid Ingres retrospective at the Louvre, the first in 40 years, shows how hard it is to classify this great artist, writes Lara Marlowe

Jean Auguste Dominique Ingres (1780-1867) lived through three French revolutions, three monarchies and two empires. He showed an extraordinary ability to adapt to successive regimes. First he glorified Napoleon Bonaparte in a neo-Byzantine portrait so opulent that it was ridiculed in the Salon of 1806.

"What horrors have I just learned?" Ingres said on hearing of the criticism heaped on his Napoléon sur le trône impérial. "So the Salon is the theatre of my shame? I am the victim of ignorance and bad faith." Two hundred years later, the injustice has long been righted. Napoleon is on exhibit in a splendid Ingres retrospective at the Louvre. The first in 40 years, it explores all aspects of the artist's work - portraits, drawings, watercolours, religious paintings and nudes.

If the 79 paintings and 101 drawings prove anything, it is the impossibility of classifying this great artist. Like his teacher David, Ingres was a neo-classicist; like his rival Delacroix, a romantic. But he was also a mannerist, a symbolist and a hyper-realist, whose influence continues to this day.

Ingres was so crushed by the cold reception accorded his work in 1806 that he stayed on in Italy for 18 years, not even returning to France to meet Madeleine Chapelle, the hat-maker with whom he'd struck up an epistolary romance. Instead, she came to Rome, where the couple married in 1813. It was a happy union, lasting until Madeleine's death 36 years later.

Ingres befriended Napoleon's sister and brother-in-law, Caroline and Joachim Murat, newly crowned Queen and King of Naples. They commissioned Ingres' Odalisque, doubtless his best-known masterpiece. In tribute to Murat's participation in the Egyptian campaign, Ingres accoutred the reclining beauty with a turban and oriental jewellery, a hookah pipe, incense, and peacock feather fan.

Six years earlier, in 1808, Ingres had painted La Baigneuse Valpinçon. She too was shown from the back, in a pose that would later be imitated by Renoir. The bather also wore a turban, and has let her Turkish slippers fall beneath her feet.

Today, Ingres' nudes, with their creamy, velvet skin, inviting cushions and rich draperies, are considered among the most sensual in the history of painting. But they were savaged by early 19th-century critics.

Ingres called anatomy "a dreadful science, a horrible thing I cannot think of without disgust". The interminably long back of his Odalisque allegedly has three too many vertebrae. The sublime Baigneuse Valpinçon seems to hide her atrophied legs in shadow; once you've noticed the defect, it is difficult to ignore it.

Ingres lived long enough to see the critics' taste transformed. Nearly four decades later, in 1852, Louis de Cormenin wrote: "No one knows the neglected art of the nude better than , knows the secret beauties of woman. No one softens a throat more lovingly . . . He takes women by surprise from every angle, the most elegant and the most sensual."

Once of Ingres' last masterpieces, Le bain turc (1859-1863), was inspired by letters from the wife of an ambassador to the Sublime Porte. Ingres was nearly 80 years old when he imagined this scene from a Turkish harem, where naked beauties dance, play music and fondle each other.

Picasso painted his own version in Les Demoiselles d'Avignon. Distraught though he was over Madeleine's death, Ingres remarried three years later, at the age of 71. His second bride, Delphine Ramel, was 43.

Art and love seem to have preserved him. "The older I grow, the more my work becomes an irresistible need for me," he said.

Ingres' vitality in old age was legendary. Well into his 80s, the chronicler Edmond de Goncourt wrote, "when Ingres started to feel aroused by a dancer at the Opera, he exclaimed, 'Madame Ingres, to the carriage!' and he did the deed on the way home."

Going to the Opera was also a way for Ingres to fill his order book. He was haunted by the memory of hard times, especially after the fall of Napoleon I, when he and the first Mrs Ingres scrimped by in Italy on Ingres' pencil portraits of British tourists who had resumed the "grand tour" after the Napoleonic wars.

Ingres' career was saved by the Restoration. His canvas of Louis XIII placing France under the protection of the Virgin was the triumph of the 1824 Salon, and marked the reconciliation of king, church and country. The following year, King Charles X made Ingres a chevalier de la Légion d'Honneur.

Ingres so adored Raphael that he wept when he contemplated the Renaissance genius's work. Ingres gave many of his Virgins - and Odalisque - the face of Raphael's Fornarina. But despite the startling sensuality of his Madonnas, Ingres' religious paintings seem lost in no-man's land, between the Renaissance and the now unfashionable, gaudy 19th century Saint-Sulpice school.

Ingres was motivated by the need for recognition and extreme perfectionism. "I am tormented by an insatiable desire for glory," he said.

His life was a pendulum of pain at the incomprehension of public and critics, and joy when he was honoured.

When Le Martyre de saint Symphorien flopped at the Salon of 1834, Ingres packed up and went back to Rome for six more years, this time as director of the Académie de France, the government-run artists' refuge also known as the Villa Médicis.

In Rome, Ingres indulged his passion for music, playing his violin with Paganini and Cherubini, whose portraits he drew and painted. His musical talent gave the expression violon d'Ingres to the French language, meaning a hobby. The surrealist photographer Man Ray put music holes on the back of a model resembling the Baigneuse Valpincon and called it Violon d'Ingres.

Encouraged by the new-found patronage of the Duc d'Orléans, Prince Ferdinand-Philippe, Ingres returned from exile in 1841 and was feted with a banquet for 400 people.

Prince Ferdinand-Phillipe was killed in an accident the following year. He was the Princess Diana of his day. France went into an orgy of mourning, and Ingres' portrait of the young prince became an iconic image that inspired Édouard Manet's Fife Player.

Throughout the 1840s and 1850s (when his allegiance shifted effortlessly from the house of Orléans back to the Bonapartes) Ingres was to French high society what his teacher David had been to the court of Napoleon I - the favoured painter of French aristocracy.

Ingres was made a senator and promoted to the rank of grand officier de la Légion d'Honneur. An entire room was reserved for his work at the 1855 world's fair, where his Princesse de Broglie was hailed as a masterpiece. It had taken Ingres three years to paint the symphony of white flesh, blue and gold satin, lace and pearls.

Ingres was apparently as poor a judge of his own work as were the critics of his day. He valued his large narrative paintings on Biblical, mythological and classical themes more than his portraits. "Cursed portraits which always prevent me from getting to the great things that I cannot do more quickly," he said of them.

Yet the portraits are what has remained. From the Rivière family, painted in the first decade of the 19th century and shunned along with Napoléon and the Baigneuse Valpinçon, to the French civil servants who administered Napoleonic Italy, to the aristocratic ladies of the July Monarchy and Second Empire, Ingres captured the character of his century.

Each painting tells a story worthy of Balzac or Stendahl: Caroline Rivière, painted in 1805, like a white lily in the countryside, would die within a few months of her portrait. Louis-François Bertin, owner of Le Journal des débats, opposed Napoleon in the name of the Republic. He has the powerful, piercing stare of a newspaper editor, his hands on his knees like an eagle's talons. Picasso's portrait of Gertrude Stein would later mimic Bertin's posture and massive physique.

For sheer, breath-taking virtuosity, nothing can equal the room where curatorshave hung five Ingres portraits of the women who, Théophile Gautier said, characterised la grande dame moderne: Vicomtesse d'Haussonville, Baronne Betty de Rothschild, Princesse de Broglie and Madame Moitessier. The clothes, jewels and settings are sumptuous, the expressions on the faces at the same time haughty and come-hither.

Ingres (1780-1867) is at the Louvre until May 15. Wed, Fri and Sat 9am-10pm, Mon, Thurs and Sun 9am-6pm, closed Tues