Not in the way the current system works because the publishers are doing nothing, they are just taking the papers as reviewed by the committee as-is.
In fact, with this law, we are most likely going to see is that the universities will automatically hook into something like: https://hal.archives-ouvertes.fr/
When you submit a paper to a journal, your university normally request that you submit your paper to the internal university store. This store will then automatically push your paper to this open access library after X months.
If this moves this way, publishers would have to say: French researchers cannot publish with us any more....
Not directly, but wouldn't it open up a box of issues where publishers make it harder for authors who distribute their papers for free to get published the next time around?