I am an American living in France, have a french visa, and plan to go to Cuba via Madrid using my American passport. Should I expect any problems and can I get a tourist card from Madrid?
As Anya says your Passport is immaterial, Cuba welcomes everyone - especially Americans - with open arms.
You MUST have a Tourist Card before boarding the aircraft in Madrid. Impossible to guess what your options are when you give no clue regarding which airline or whether you're on a package tour or travelling independently, but call your airline and confirm whether they supply the Tourist Card. If not, you need to explore options.