I was looking for one for a while, but a lot of Météo France's data has been behind paywalls for a long time until some open data laws changed that, so an official machine-readable format is not what they would tend to provide. Now that feeds considered to be obsolete for the general public because they all moved on to social media and newsletters, it's very unlikely that they are going to consider starting one.

Fortunately I have been going down a rabbit hole (for five minutes a month of course) on an XML standard for alerts that I have seen in use by various weather services or disaster management agencies, which will someday lead to a whole bunch of RSRSSS posts on that standard and its uses. And that got me to find the closest thing to an official feed we can have, since it is provided by a service of the European Network of National Meteorological Services: RSS 2.0, Atom

It reports all warnings in English for all departments. While the website does allow to view the details for each department, that's not handled in the feeds, so you will have to use your feed reader's filtering features to pick what you want.