When there is an equivalent car to a Toyota that's offered from Peugeot, Renault, or Citroën, or possibly Fiat or VW - French people will buy that instead.
France is one of the few markets where there's still a distinct resistance to Japanese cars. Like most foreign-issues in France, that's down to wanting to preserve things French rather than any issue with the actual products.
Now that PSA and Renault are two of the most powerful and profitable companies in the Automotive world, I'd say that the French have less to worry about than they did in, say, 1990 - when it looked like both would probably collapse under an expected Japanese invasion. That didn't happen - and in the time that the French bought their automakers by refusing to drop import quotas until 1996 they gave their domestics an opportunity to turn things around, and turn around they have.
The Aygo is a good car but the French will never buy it when they can get a Citroën or Peugeot instead that's basically the same thing. Similarly, they'd rather have a Laguna than a Primera, etc.
Chinese manufacturers will face hard resistance to their products in France and probably in Spain and Germany too. The fact that you can get a car like a Fiat Panda or Toyota Aygo for not much more than an outdated Daihatsu clone from Geely means that few will be tempted. For the ultra-cheap class of car, the micro, France has it's own class of driver who wants a car like that and they by Ligiers. They won't defect either, despite the fact that even some of the worst Chinese cars are probably just as good or better than the tiny Ligier.
America is a better target. Fewer small cars to compete against, dramatically rising fuel prices, and a much bigger pie overall.
If the Chinese play here in America it's worth noting that it will finally force Fiat and PSA to return here or risk global decline.