There was a delicate balance between "getting expendable manpower" and "arming the next colonial uprising". Both France and England did raise armies from their colonies; however they were mainly second-line units without heavy weapons. Their main use was for colonial garrisons - the usual method was to pick a tribe to recruit from, use that tribe to keep other tribes in line, and use privileges and the threat of European formations with heavy artillery and machine guns to keep your native soldiers in line. So their main effect was to allow garrisoning Africa relatively cheaply, without tying up valuable regular troops. An exception is the fighting in German East Africa, largely fought by such native troops.
The French did use Senegalese units on the Western front, apparently even in a shock/assault role; this may indicate that what I said above applies mainly to England and that France had a different approach, or that Senegal was special for some reason. The British also tried to use units of their Indian Army on the Western Front, but found it hard to reinforce them after the heavy casualties of the initial battles; additionally the Indian troops were not well equipped for European winter. They were withdrawn in December 1915 and fought in Mesopotamia for the rest of the war.
I should note that in all these cases, the ratio of soldiers to colonial population was tiny compared to Europe, where there was a draft. Colonial soldiers were by-and-large volunteers, and recruited from a subset of the population at that; again, the imperial powers did not want too many of their subjects to have military experience. In WWII the Indian Army reached 2 million; in the Great War there was a single Indian Corps of two divisions. (Of course, some units had to be held back to guard the Northwest Frontier.) There was no question of mobilising colonial manpower on anything like the scale of the metropolitan armies.
Yes, both France and the UK raised troops in their colonies both to fight in "less important" theatres of the war and, in some instances, shipped some of those men to Europe to fight.
The French had the famous Senegalese Tirailleurs, made up of men recruited from French West-, East-, and Central-Africa (i.e. not just Senegal), many of which ended up fighting on the western front.
The British recruited troops from Africa as well. However, the British did not use African soldiers in Europe - though they did see action in both Africa and the Middle East. More important for the British were troops from India: over a million men from the Indian Army served overseas during WW1, including approximately 130,000 on the Western Front. Other Indian expeditionary forces saw action in Egypt, the Middle East (including at Gallipoli), Africa, Russia (fighting the Soviets after the revolution), China (seiging German possessions in China), amongst others.