The French Colonial Empire

The French Colonial Empire existed from the 1600s to the 1960s, roughly the same length of time as the British Empire lasted. The French colonial empire's possessions included:

Canada: Much of it. Nowadays, the only French-speaking part is Quebec. Also kept the islands of Saint Pierre and Miquelon just off the coast of Newfoundland.
United States of America: Parts of it (which explains patently French place names like Des Moines, Saint Louis or Louisiana), although the fledgling American government bought up much of this area in the Louisiana Purchase. (The French sold it to the Americans so they'd be strong against Britain.) Well, that and the fact that Napoleon had bills to pay, since beating up the rest of Europe didn't come cheap.
Much of the Caribbean, including: Anguilla, Dominica, Grenada, Haiti and Saint Vincent and the Grenadines (which, incidentally, would be a good name for a jazz band).
Much of western Africa, in two parts:
- The Arabic-speaking lands of North Africa, namely Algeria, Tunisia, and Morocco. As you might have guessed, these colonies (particularly Algeria) are mostly Sahara Desert, but the coastal areas provided lucrative and strategically-useful ports for France.
  - Tunisia and Morocco were technically protectorates, officially governed by traditional Arab monarchs (a Sultan in Morocco and a Bey or Lord in Tunisia; both upgraded themselves to King upon independence), but that didn't really mean much. They were colonized relatively late (Tunisia in 1888, Morocco in 1912), and the French influence on them, while significant, did not do substantial damage to the native Arab-Berber culture. Morocco is rather interesting in that it was not entirely under French control; besides the Western Sahara/Rio de Oro (a whole 'nother can of worms), northern Morocco was a Spanish protectorate, with the exception of Tangier (right across from Gibraltar), which was an international free port.
  - Algeria was colonized quite early (in 1830) and governed as an integral part of France, divided up into departments, and colonized by Frenchmen (known at first as colons, later as pieds-noirs (lit. "black feet")). These immigrants had disproportionate clout in the National Assembly (their MPs and Senators stayed in office for longer than usual, giving them incredible seniority), meaning that when the Arabs started to revolt against French rule in 1954, the Fourth Republic found it very difficult to compromise. The war that resulted was thus extremely bloody (Arabs still call the Algerian War of Independence the "War of a Million Martyrs") and lasted until 1962, when Charles De Gaulle finally granted Algeria its independence. To this day, Algeria is probably the most culturally messed-up country in North Africa; the French successfully played off Arabs and Berbers against each other, and Algerian Arabic has enough French that other Arabs find it even harder to understand than other forms of Western Arabic (which is notoriously difficult for Eastern Arabs already).
  - What of the pieds-noirs? The new Algeria gave them a choice: suitcase or coffin. Most of them went to France, where the mainland French were not thrilled to see all the "immigrants" looking for jobs and such. The pieds-noirs, meanwhile, were taken aback by their lukewarm reception in what they had always considered their own fucking country. It was an ugly chapter in French history, and no one much likes talking about it.
- French West Africa, consisting of modern-day Mauritania, Senegal, Mali, Niger, Burkina Faso, Togo, Cote d'Ivoire, and Guinea. the northernmost colonies were mostly desert (the Sahara, specifically) and dry plains and Muslim, while the southern ones were wetter (often rainforest) and mostly followed traditional African religions (many converted to Christianity). Again, it was mostly coastal ports the French were after, although they were also searching for minerals. Being proper colonies, the fight for independence wasn't terribly bloody (if at all, in many places); World War II having drained France's resources, the case for losing these African colonies was painfully clear.
There was also French Central Africa, from Chad down to what are now the Central African Republic, Congo-Brazzaville, Gabon, and much of modern Cameroon (the rest was ruled by Britain). Same old story: Chad and a fair bit of Cameroon were dry and Muslim, the rest were wet and traditional/Christian (Christianity had been spread in Congo by the Portuguese in the 16th century).
A few scattered colonies in East Africa, including the amusingly-named Djibouti (say it out loud) in the Horn of Africa (across the Strait of Aden from Yemen, making it deliciously strategic), which was then called French Somaliland; and Madagascar (which should be self-explanatory).
Cambodia, Laos and Vietnam, collectively known as French Indochina. The first Vietnam War was fought to try and retain these.
Unofficially part of the Empire was Lebanon, which was part of the Ottoman Empire, but its Christian population (a majority at the time) was under French protection. After the end of World War I, France split the Middle East with Britain under a system of League of Nations "Mandates": Britain got Palestine (including the Transjordan) and Iraq, while Lebanon and Syria came under French rule. This lasted until shortly after World War II, but as far as the locals were concerned, it might as well have been a century. Much to their chagrin, the oil the French had hoped would be in Syria failed to turn up (it was all in British Iraq. D'oh!).

Many of these countries are part of the Francophonie, somewhat like the British Commonwealth.

France has retained somewhat more minor colonies than Britain, but has directly integrated them into the core state rather than running them as separate dependencies. The largest of these are New Caledonia and French Guiana, the latter noted for being the site of the European Space Agency's launch site at Kourou.