The men-in-suits at LFAT
I presume you mean the Douane who are the Immigration/Customs Police and wear uniforms
It is very unusual for a Frenchman to carry a passport. All Frenchman have ID cards. It is very unusual, for a French person, not to have it with them, even when travelling throughout the EU. Not carrying ID could always arouse suspicion from the police. ID is always being asked to be shown, for various everyday reasons: in Post Offices and collecting orders in shops. I too have an ID card, being a permanent resident in France, and no longer ever carry my passport unless it is specifically asked for. I always carry my Residents Permit (ID)
Le Touquet is a port, and in these times, perhaps, it is a reasonable step up in security, possibly a temporary one. On the other hand the Douane at Le Touquet have been notoriously inconsistent for, at least, the last 50 years or more. Sometimes they are at their post and sometimes they are not. Sometimes you are just waved through and sometimes you are not, as it suits them.