If I am bound for Paris from Mombasa, Kenya and I transit through Amsterdam or Istanbul, do I need a transit visa or will my Schengen visa suffice?
Having a uniform Schengen visa (Visa C) obviates the need for a transit visa within the Schengen area in most cases.
If you transit through Amsterdam, you will have to go through passport control at Amsterdam itself. Your Schengen visa will allow you to enter the Netherlands, from where you will be able to travel onward to Paris without further visa checks.
Turkey does not require a transit visa as long as you stay within the airport transit area. Therefore, if you're transiting through Istanbul and don't plan to leave the airport, you will simply be transferred to your connecting flight (no visa required), and can use your Schengen visa to enter France when you reach Paris.