The water heating system in France is usually of the main water pressure type. This means that water from your meter feeds your tank that has an electric immersion heater inside to heat said water to temperature (there should be a dial on your tank (called cumulus in France) to adjust water temperature up or down).
When water is heated, it expands….that’s why there is water “leaking” through what is called the “valve de securite”. This drip is normally collected by a 32mm pipe fitted with a collector that takes the water away to be discarded. In your case, someone has put a bucket….nothing wrong with that, I have had it for years in a previous house (just remember to empty the bucket from time to time).
If you did not “drip water”, the weakest part of your piping would give way under the built-in pressure with rather negative consequences.
If you had an immersion heating system in the UK or anywhere else in the world for that matter, you would find out that works about the same…..generally, if you add cold water to hot water in a container, the temperature of the water inside reduces……..You might have already heard screams in a household referring to “Mum….there’s no hot water left….”
As a solution, you either invest in a boiler that delivers hot water instantly and on demand (called combi-boilers) or you adjust the temperature gauge of your cumulus to a higher setting (60c maximum).