I am an American citizan looking to purchace a home in France. What happens to my citizanship here in America? Can I work in France?

Nothing.

You may retain your American citizenship and live and work in France.

And you could get dual citizenship b/w the 2 countries as well.

Are you a European citizen ?
If, not, then you will need a visa to work in Europe. This can be a difficult procedure, as it is for Europeans to work in the US.
Are you married to a European ?

This might help :

http://www.amb-usa.fr/consul/acs/guide/default.htm