In this instance, the price cap is working exactly as intended. The state pushes Total to introduce a price cap by threatening a windfall tax on the industry as a whole. Total accepts, and introduces a voluntary price cap, selling at the below-market rate in a first-come-first serve regime (which it can afford to do, as it's an integrated producer). Total serves fuel to the majority of motorists at the below-rate price. When Total runs out of fuel, motorists who do a lot of travelling then need to pay the above-market rate at E.Leclerc instead.

Without introducing an unpopular tax regime, the French govt has found a way to progressively increase prices for higher mileage motorists. Supplying most motorists at a reasonable price, while having high-mileage motorists pay the unsubsidised price for most of their petrol.