Wiki is full of the info you need. I have copied snippets but you really ought to read the whole article.
In southeast Asia Napoleon III also established French control over Cochinchina (the southernmost part of modern Vietnam including Saigon) in 1867 and 1874, as well as a protectorate over Cambodia in 1863. Additionally, France had a sphere of influence during the 19th century and early 20th century in southern China, including a naval base at Kuangchow (Guangzhou) Bay.
It was only after the Franco-Prussian War of 1870–1871 and the founding of the Third Republic (1871–1940) that most of France's later colonial possessions were acquired. From their base in Cochinchina, the French took over Tonkin (in modern northern Vietnam) and Annam (in modern central Vietnam) in 1884-1885. These, together with Cambodia and Cochinchina, formed French Indochina in 1887 (to which Laos was added in 1893, and Kwang-Chou-Wan  in 1900). In 1849, the French concession in Shanghai was established, lasting until 1946.
Influence was also expanded in North Africa, establishing a protectorate on Tunisia in 1881 (Bardo Treaty). Gradually, French control was established over much of Northern, Western, and Central Africa by the turn of the century (including the modern nations of Mauritania, Senegal, Guinea, Mali, Côte d'Ivoire, Benin, Niger, Chad, Central African Republic, Republic of Congo), and the east African coastal enclave of Djibouti (French Somaliland).
The French made their last major colonial gains after World War I, when they gained mandates over the former Turkish territories of the Ottoman Empire that make up what is now Syria and Lebanon, as well as most of the former German colonies of Togo and Cameroon. A hallmark of the French colonial project in the late 19th century and early 20th century was the civilizing mission (mission civilisatrice), the principle that it was Europe's duty to bring civilization to benighted peoples. As such, colonial officials undertook a policy of Franco-Europeanization in French colonies, most notably French West Africa. Africans who adopted French culture, including fluent use of the French language and conversion to Christianity, were granted equal French citizenship, including suffrage. Later, residents of the "Four Communes" in Senegal were granted citizenship in a program led by the Afro-French politician Blaise Diagne.