Nothing's crossing the border in this case other than information. It's more like a guy on the French side of the border shouting over to a guy on the Swiss side, and the French government trying to regulate what the guy on the Swiss side is allowed to say in reply.
Regardless of what analogy you use, the point is that the company isn't in France, it's in Switzerland. It doesn't make sense for it to have to do anything to comply with French law, even if it's interacting with someone who happens to be in France.
None of these analogies work very well because providing services across the border without crossing it doesn’t scale very well in-person. I should have just said that directly, but the image of cross-border bagel service was too funny to pass up.
WRT your second paragraph, I think I addressed it already in my second paragraph.