Is the expression, "to get a rise out of" related to the word, risable? Both could come from the Latin ridere, as does the French word, rire, but what about the expression?
Did it originally mean, "to make one laugh?"

The expression "get a rise out of" is according to the OED a Scottish use of rise meaning "A joke; a trick played on someone." This is a use of the noun rise which has a lot of meanings to do with rising up or upward movement. It is Germanic in origin and related to raise and to German reisen "to travel". It's not related to Latin rīdeō as far as I can see.