The flag of Paris is half of the French flag, and that is not a coincidence. The city's vertical bicolor, blue at the hoist and red at the fly, carries colors Paris has claimed since 1358. When revolutionaries needed a cockade in July 1789, they reached for those two colors and set the monarchy's white between them. The tricolor that resulted conquered the world's flagpoles; the parent flag stayed home, flying over the Hotel de Ville with a silver ship at its center and one of the great civic mottoes attached, though the motto, strictly speaking, belongs to the coat of arms and not to the flag at all.
Blue and red since 1358
The colors enter recorded history with Etienne Marcel, the provost of the merchants who led Paris in revolt against the crown in 1357 and 1358. His partisans wore hoods of red and blue, and the pairing stuck to the city. Tradition backfills a saintly explanation: red for Saint Denis, the first bishop of Paris, beheaded on Montmartre and patron of the royal abbey north of the city, and blue for Saint Martin of Tours, the Roman soldier who cut his cloak in half for a beggar. Blue cloaks and red martyrdom make a tidy story, and like most tidy heraldic stories it was probably composed after the fact. What is certain is the date: the city has answered to blue and red for almost seven centuries.
A plain flag of the two colors, without ornament, existed by the eighteenth century. The version the city government actually flies today adds the full coat of arms at the center of the bicolor and follows 2:3 proportions; the naked bicolor remains correct and turns up in square form as well.
A ship for a city of boatmen
The arms in the flag's center are older than the flag and nearly as old as the colors. Paris began as an island city living off its river, and by 1170 the Marchands de l'eau, the watermen's guild, held a royal privilege over commercial navigation on the Seine between Paris and Mantes. Their seal, recorded around 1210, showed a river boat. The guild's chief, the provost of the merchants, gradually became the head of the city government (Marcel held exactly that office), and the boat sailed from the guild's seal onto the city's arms, first recorded in 1358.
The blazon is simple and has barely moved since the Middle Ages: on a red field, a silver ship in full sail on waves; above it, a blue chief sown with gold fleurs-de-lis, the badge of the French crown, in which Paris sat as capital. Revolutionary governments abolished heraldry along with everything else in the 1790s, and the arms went dormant before returning in the early nineteenth century. The ship has since accumulated a mural crown, supporters of oak and laurel, and the city's decorations, but the core image is still a boat that any thirteenth-century Seine bargeman would recognize.
Tossed but not sunk
Beneath the ship runs the motto: Fluctuat nec mergitur, "she is tossed by the waves but does not sink." The phrase shadowed the boatmen's emblem for centuries, appearing on Parisian jetons and coins in the 1580s, before Baron Haussmann, prefect of the Seine, made it the city's official motto on November 24, 1853, just as he began demolishing and rebuilding much of the city the motto described.
The distinction matters for flag purposes: the motto belongs to the arms. The flag itself is the blue and red bicolor, mute; only when the full achievement of the arms is displayed, on the flag or off it, does the Latin appear on its scroll. Parisians largely ignored the fine print for 162 years, until the night of November 13, 2015, when coordinated attacks killed 130 people at the Bataclan and across the city's east. Within days Fluctuat nec mergitur was on murals at the Place de la Republique, on projections, posters, and skin. A centuries-old boatmen's boast became the city's public answer to terrorism, and the coat of arms, normally the least noticed piece of municipal furniture, was suddenly legible to everyone.
The tricolor connection
The flag's largest legacy is the one it wears anonymously. In July 1789, as Paris armed itself, the new militia adopted a cockade in the city's blue and red. The white of the Bourbon monarchy was added between them, by the standard account at the urging of Lafayette, commander of the new National Guard, to bind king and city together. The three-colored cockade became the emblem of the Revolution, and its colors, run as vertical stripes, became the French national flag.
So the French tricolor reads, from hoist to fly: blue of Paris, white of the monarchy, red of Paris. The city's flag simply omits the middle. In practice you will see the two flying together at the Hotel de Ville and the arrondissement town halls, usually with the European flag for company, the national banner and its municipal parent side by side. Few cities anywhere can watch their own colors fly twice on the same building.
References
[1] "Flag of Paris," Wikipedia. https://en.wikipedia.org/wiki/Flag_of_Paris
[2] "Coat of arms of Paris," Wikipedia. https://en.wikipedia.org/wiki/Coat_of_arms_of_Paris
[3] "Paris (Department and Municipality, France)," Flags of the World. https://www.crwflags.com/fotw/flags/fr-75.html
[4] "Paris coat of arms and motto's history," Travel France Online. https://www.travelfranceonline.com/paris-coat-of-arms-and-mottos-history/