He should see a doctor, but getting a man to do so when he doesn't see the need is well-nigh impossible.
If you are holidaying in France, make him promise you he will go to his doctor when you get home.
If you live in France, I would suggest you find someone who speaks good English - a school-teacher teaching English, perhaps, and get her or him to write down exactly what you have described here of symptoms and when they occured, that your husband suffers from astma, and that he has pooh-poohed the very thought of going to a doctor.
Get this person to write down exactly what you need to say if you phone either for an ambulance or an emergency doctor, and to coach you in pronouncing it correctly.
And if you are living in France, please do find someone who can teach you more French, so you can deal with this sort of thing confidently yourself, as far as explaining what is wrong and understanding what you are being asked or told.