The achievement of the French painter Eugène Delacroix — the Romantic paragon of 19th-century French art — is like a huge puzzle whose pieces don’t easily fit together. But at least we finally have a chance to try to make them cohere.

The first full-dress retrospective in North America devoted to this complex, enigmatic, foundational figure, titled simply “Delacroix,” opens on Monday at the Metropolitan Museum of Art. Organized with the Louvre Museum in Paris, where it appeared in fuller form this year, the Met show presents nearly 150 paintings, prints and drawings in a dozen large galleries whose arrangements sometimes have the clarity of individual exhibitions. Some of his biggest, most famous paintings are staying home, but enough prized Delacroixs from the Louvre, other French museums and elsewhere — including the hypnotic “Women of Algiers in Their Apartment” and the grim “Greece on the Ruins of Missolonghi” — are on hand to account for an astounding career.

As Picasso told the painter Françoise Gilot: “That bastard. He’s really good.”

And yet this precocious prophet of the modern age does not conform to our ideas of unalloyed progress. While he opened the door to Modern painting as a process, he kept it tightly closed to modern life.

The show has been assembled by Asher Miller, associate curator of the Met’s department of European paintings, with Sébastien Allard, the director of the Louvre’s department of paintings, and Côme Fabre, its curator. Their selections give us, in largely chronological order, Delacroix the talented student; the portraitist of his loved ones and of big cats; the illustrator; the misogynist bachelor and Orientalist; the frequent star of the Paris Salon; and the painter of religious commissions and of slightly naughty (but highly salable) troubadour paintings.