The stereotypical French speaker who has trouble with English [h] would definitely have the same problem with the Japanese [h], [ç] and [ɸ]. If they can't manage the tongue placement for English [θ], how are they supposed to handle Japanese [ɕ] and [ʑ]? And that's just the consonants.
Usually when someone thinks that language X has all the sounds of language Y, it's a speaker of language X who hasn't yet realized that their ears are too attuned to language X to recognize the sounds of language Y as something different. Don't trust your ears!
