Heat pumps are sold in France, and I think you'll find they are common around the mediteranean, where it doesn't get too cold in winter. Maybe for the reasons stated above, they don't get installed too much in central France where the winters are colder.
If all your heating is currently electrical then it should cut the fuel bill once installed, but are you sure you'd not be better off with something else.
I visited a house a few months ago where they had black solar panels containing liquid, not solar cells, and if the liquid outside was warmer than the liquid inside, the pump would turn on and bring the heat into the house. The house had underfloor heating. They could also heat water for showers, washing up, etc from the panels too.
There are newer evacuated tube designs where a black blade about 4 inches by a yard warm up with light (even on cloudy days to some extent). A tube runs down the centre of the blade, taking the heat from it, and the tube contains just a few cc's of water. So water temperatures are pretty darn hot. Since the tubes have a vacuum in them the black blades won't get affected by cool rain like normal solar panels.
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Okay, the UK has the gulf stream to keep it warm, but I think you need to check how well the heat pumps work when it gets cold.
I've rejected the idea for my girlfriend's house in central France and it has 2500m2 of garden to run tubes round underground to capture heat, and a constant ground temperature of about 13°C if you go down a bit, like wine cellar depth.