You could get Interrail but there's no advantage: you could travel on 2 days max in your country of "residence" (would be France for you).

Get Eurail, it's exactly the same price converted (one in USD and one in €). Use your American passport with it.

The thing is want to travel to like 3-4 different countries 

Don't know what that does mean. The only difference between Interrail is in France.

With Interrail you are restricted to max. two travel days in France. With Eurail there is no restriction. 

If you do not visit France it doesn't matter. 

You may buy Interrail with your french passport and you may buy Eurail with a US proof of residence. Eurail is better if you do visit France, too.