Confusing as this may sound, the military forces used to expand and defend France's colonial empire were divided into two distinct groups.
The
Armée d'Afrique (which included the Foreign legion, the zouaves, the
tirailleurs algériens/tunisiens/marocains, the
bataillons disciplinaires d'Afrique/
infanterie légère d'Afrique, the
chasseurs d'Afrique and the spahis) was stationed in North Africa and was technically a part of the Army, being attached to the Ministry of War. Although these troops took part in just about every colonal expedition undertaken during the third republic, they weren't used to garrison the colonies once the fighting was over : they simply returned to their bases in North Africa after military operations ended.
The true colonial forces, or
troupes coloniales, were originally raised and administered by the Ministry of Navy, which also ran the French colonial empire. The naval infantry, or
infanterie de marine, was composed of white French metropolitan soldiers who effectively stopped being marines after 1846 (armed sailors, or
fusiliers-marins, took on that role from the mid-C19th onwards and regularly provided naval brigades for short-term land operations). The other component of the colonial army were the native soldiers raised throughout the empire and known as
tirailleurs indigènes. The
Tirailleurs tonkinois and
Tirailleurs annamites shown above were raised in French Indochina and Cochinchina, while Africa relied on its
Tirailleurs Sénégalais, which weren't all Senegalese in any case (
tirailleurs sénégalais became the generic name given to all black infantrymen used in both the AOF and AEF -
Afrique Occidentale Française and
Afrique Equatoriale Française, i.e French Western Africa and French Central/Equatorial Africa). The African colonial establishment also included mounted native units soon known as Senegalese Spahis, not to be confused with the spahis of the
Armée d'Afrique who were Arabs and not negroes.
In 1900, the whole of the
troupes de marine were withdrawn from the naval establishement and placed under the authority of the Ministry of War, taking the
troupes coloniales name in the process.
In terms of deployment, major military expeditions such as the conquest of the Tonkin in the 1880's, the Dahomey expedition of 1892 or the invasion of Madagascar in 1895 usually involved a combination of colonial troops and
Armée d'Afrique units. The Foreign Legion and the Naval Infantry usually provided the bulk of the force, with additional contingents being drawn from the zouaves, the turcos, the colonial native troops and whatnot. On the other hand, small-scale expeditions and internal security operations in western and central Africa tended to be conducted almost solely with native African soldiers (though their officers and senior NCO's were obviously white Frenchmen), mostly Senegalese
tirailleurs and spahis.

The uniforms worn by these troops evolved considerably between 1870 and 1920. White soldiers started out with second empire type dark blue uniforms until more practical khaki - or proto-khaki - garments started appearing in the 1880's. The Naval infantry in particular experimented with a series of campaign uniforms in the 1880's and 1890's - with varying degrees of success - before settling for khaki in 1900. Similarly, the tirailleurs sénégalais adopted khaki at the same time (the zouave trousers shown above by former user were a full dress item used only for parades, by the way : short tight trousers were used in the field instead). Given the variety of uniforms used in the period, it would be rather fastidious to list them all here : just tell me which specific units and which decade you're interested in and I'll see what I can dig up.
Hope this helps a bit