You were wrongly informed, so we suggest telling the school or trying a different one.
The official French government website service-public.fr states that it is possible to follow the seven-hour training for car licence-holders if you hold a licence from an EU country (so this may not be possible after Brexit and any transition period).
Other EU states’ licences are deemed the equivalent of a French licence and there is no obligation to swap them for a French licence to use while living in France and no reason not to take the scooter course.
Your UK licence must, of course, still be in its validity period. Find a session with a local provider with internet terms such as formation 7 heures 125 and the name of your local town.
Another condition is that you should have passed your car driving test more than two years ago.
There is a theory session about road safety and responsible riding and an outing in town traffic and outside in the countryside.
At the end of the course you receive a certificate, which you need to carry with you when using a scooter.
Send your queries about life in France by email to email@example.com