As Norman indicates, there are strict rules regarding the employment of non-EU nationals. You can't even start the application process for a French work visa until your potential employer has sought and obtained authorization to employ you. It's unlikely that such authorization would be forthcoming if you were seeking to fill any job vacancy which could otherwise be filled by an EU citizen:
http://www.ambafrance-us.org/spip.php?article3 60
Similar rules are likely to exist throughout the EU. That's because (apart from a few transitional restrictions) any EU citizen is free to live and work in any of the 27 member countries. So a Brit, a Pole, a Dane or a Latvian must, quite rightly, be given precedence over a US citizen when employment is available in France, Spain or elsewhere within the EU .
Chris