There is a common misconception that you must use only one passport for any leg of a journey, from start to finish. It's possible that there are some cases where it may be true, but in general it is not. My source for this is dozens of flights between the US and the EU as a dual US/EU citizen.
Your asking this question suggests that you may not be aware that the US has a law that essentially requires US citizens to use their US passports when they enter the US.
I suppose that leaving France and entering the US I will show my US passport, ...
No; when you leave France, you'll show your US passport to the airline and your French passport to the passport control officer.
but on my trip back to France, do I show my French passport - without or with an ESTA?
You should show your French passport to the airline. Depending on what airline you fly, they may or may not care about your US immigration status. I mostly fly to Europe on European carriers, who seem not to, but I've heard stories of airlines checking visas on the way out. I've encountered it firsthand only once, on a flight operated by a US carrier. The destination was in Africa, and I was using my US passport, so it was an issue only for my wife.
If anyone does ask about your immigration status after you show your French passport, you can just say "I'm a dual citizen" and show the US passport at that point.
You will not normally encounter US government officials as you leave the US, but they do occasionally do spot checks. If that happens, you can of course show your US passport to show that you are not in violation of immigration law.
You could show your US passport when you check in, especially if your ticket indicates a stay shorter than 90 days, because US citizens don't need a visa to enter the Schengen area. But once the EU implements ETIAS, their ESTA-like program for the Schengen area, that becomes more complicated.
Regardless of what passports you've shown to anyone at any other point, show your French passport when you enter the Schengen area.
If it's without, police/customs might ask me how I entered the US without an ESTA.
Actually, ESTA authorization concerns only boarding an aircraft or vessel to travel to the US. It is not relevant to anyone's authorization to remain in the US, and visa waiver program travelers who enter by land do not need it. The thing that your French passport will lack, that might cause concern to someone examining it, is an entry stamp.
But if anyone looks at your French passport, notices the lack of an entry stamp, and asks you about it, you can tell them you're a dual citizen and, if necessary, show your US passport to prove it. As noted above, the person asking is most likely to be an airline employee because you're unlikely to encounter US government officers as you leave the US.
Finally, you should be aware that traveling with ESTA could be problematic. Your ESTA application might be denied because you are a US citizen, although people have posted online here to say that they have been able to get ESTA authorization even after disclosing US citizenship on the application. If anyone finds out that you're a US citizen, though, they might require you to show your US passport, since it is, as noted above, generally unlawful for a US citizen to enter the US without one. One person was not allowed to fly from Canada to the US with her foreign passport and ESTA, although I suspect that she was stopped by the US preclearance inspector rather than the airline.
There are several questions and answers here on the topic: