Expatinuk is right, there are a lot of people looking for a sweet gig like this. Good luck.
There is always a Fulbright option but extremely competitive in France and Spain. Otherwise, you would need a work permit to be legally paid in France or Spain if you are not an EU citizen and you should look into their respective requirements for securing the right to work in these places. The study abroad teaching suggested by prof_tournesol is one way to avoid the problem of the work permit if it is a US institution that is paying you.
Probably the easiest gig to get (and not that is it necessarily easy, but easier than other options) is teaching English abroad since there are so many institutes doing this around the world but France and Spain are not the easiest places to find this, you'd have better luck in Eastern Europe, Asia or the Middle East. Depending on the area of your PhD, you might be able to get this type of job even without training in ESL. It usually doesn't pay that well, but often enough to cover basic expenses (and it is easier to cover your expenses in a developing country than anywhere in Europe.) Google Dave's ESL Cafe for some resourses on this option.
You might want to check out the website for Transitions Abroad
http://www.transitionsabroad.com/ for other ideas but you will need to invest quite a bit of time to finding something along the lines you might be imagining. According to one of the links on this page, it is getting easier for non Europeans to get jobs in Europe but I don't know whether to believe that or not.