Intercept the boat, take its engine, make sure they have a few paddles and then have frogmen with those torpedo-like mini subs tow them back to 200 yards (visible distance) off the French coast.
Be harder for the French to complain or intercept if there is no surface boat doing the towing and can get the invaders back to a safe-ish distance off dry land back where they came from.
And while we are at it, load up the entire british establishment and do the same to them!
I guess the key critical-path factor in these migrant boats is outboard motors and large semi-inflatables. That would be the place the French could crack down on if they had any motive, but they are happy to let the migrants leave eh!
Funny segment on an old Yes Minister about why Britain has nukes… Because the French have got them eh!
It would not surprise me to discover the navy only has about 20 active frogmen and they are all too busy blowing up gas pipelines and dams!
Anyway would be better done by an international charity “Repatriate the invaders!” or something, so no ties to officialdom. Can imagine how difficult that would be to set up as a charity whereas a charity such as “Invaders taxi service masquerading as the rnli” is easy to maintain.