If you’re thinking about an ETA in France, you should apply to BOTH the the Fulbright ETA and the French government Teaching Assistant Program in France (TAPIF). The Fulbright awards 6 ETAs to France; the general French Government TAPIF offers an additional 1,100 positions.
To apply for both, you will need to make two separate applications, one for the Fulbright and another for the TAPIF.
For further information on the French Government Teaching Assistant Program in France, please consult the French Embassy in Washington, D.C. website: http://highereducation.frenchculture.org/teach-in-france . Note: you must be a native English speaker and US citizen or permanent resident to apply.