Rental Car in England & France

1). Doubt it would be allowed
2). A car you rent in England would have the steering wheel on the right side, which would be awkward at best in France
3). Dropping off a car in another country would incur an enormous drop off fee.

It depends on the rental company. Hertz let us rent in Portugal and drop off in Spain, with a drop off fee of several hundred Euros. Other companies (and with these other countries), you’d have to confirm with them. But it might be possible.

Not without paying a huge fee. Also the UK car has the steering wheel on the wrong side but won’t have all of the additional equipment you legally need in France that you don’t need in the UK.

But…. Why would you want to do this anyway?

you might be able to find somebody - I've never heard of it - who would allow it but if you could you would need :

a lot of money.

The ferries and Eurotunnel are not what anybody could call cheap. (I use them with my personal car) Most of the cost is for the car.

The drop charge will be horrendous - the rental company cannot rent the British car in France so will need to send a driver (£££) to go and get it and drive it back with another crossing of the Channel (£££).

You will need all the original paperwork for the car to satisfy the ferry/Eurotunnel of your right to drive it. And Customs that you won't sell it.

You will need to source French insurance. The car most likely will not be insured for the Continent (UK not in the EU any more).

You might have a dashboard switch to change the speedometer to kilometres per hour. You need that in France. Or maybe the car won't convert.

You will need to convert (often people use BeamBenders on the headlights but would the rental agency consider the residual adhesive damage a charge you?) the headlights so they don't dazzle French drivers (it is a law).

You need the equipment mentioned above not normally in a car in the UK - a reflective Triangle, high visibility vests for every person in the car, and must be in the passenger compartment, a spare lamp kit, a fire extinguisher.

Experienced drivers have little trouble driving a British set up car in France - I do it frequently - but if driving on the British side is new to you and you then want to take a British car to France it may get confusing. My first few trips I got after market mirrors for the outside of the car and for the rear view mirror. It takes getting used to.