Did they not scrap the fines for not carrying your own breathalsyer? I would say this is now more of a precaution than a requirement.
If you are going through different countries that will be a different matter altogether.
It was discussed above but the basics are
YES it is a legal requirement to carry them
But NO it is not and never has been enforced.
The proposed fine was to be 11€ but the law was passed and the date it came into force was postponed then repeatedly postponed then eventually the French government postponed it indefinitely.
There is a webpage which talks about the law in some detail but basically the man who lobbied the French government to pass this law, happened to own one of only two companies that made the kits, when the law was passed the two companies could not cope with the demand and so the enforcement of the law got postponed and then never came to be.