I am a dual citizen of US and France.
My Grandmother was a war bride and married my grandfather a US soldier, My grandmother extended it to her 5 of her children my mother being one of them and a few years ago my mother did all the paperwork to add me to the family tree.

I am currently Unemployed and have lot's of extended family in france that speak english good enough to live with them. I was wondering how difficult would it be for me to move to france for the summer and get a job? Or longer term say a year or two.

If you are a french citizen, with a french passport, then you have a right of residency in france and should be able to live in any part of the european union, including France. You might consider moving to the UK, which has a better employment rate, and speaks the same language as yourself. If you speak fluent french, you shouldn't have too much of a problem however.

I don't have a french passport, yet. My french is also pretty bad but I can learn quick.

If I did get a french passport and traveled using it, even though I am also a US citizen (first) I would still beable to live in european union? Hmm if this is possible, this present a whole realm of possibilities.