I agree with aRandomName's answer, to be clear the assumptions made in the question are wrong or at least misleading.
For what I know, one finishes PhD with only 3 years in France which is rather efficient, but one may suffer if one's research interest gets changed in the mean time, because the thesis topic is locked by the funding and by the advisor right from the beginning of the PhD, which could be disturbing in a fast changing field like cs.
While the official PhD duration is three years and naturally the funding is also for three years, the actual duration is often more than 3 years. This depends a lot on the domain and a bit on the institution. In CS the average duration was a bit less than 4 years last time I checked (probably a few years ago).
The flexibility of the topic has nothing to do with the country, it depends on the supervisor and the type of funding (by this I mean that it's more or less the same in France as in other countries). if the supervisor or funding organization has a very specific goal for the PhD, then the topic is pretty much fixed. But broad and vague PhD topics are also common, and in this case there's a lot of flexibility about the precise direction of the research. Mind also that a PhD is not as long as it seems (any PhD student will tell you that!), you don't have that much time to change your direction many times.
Besides, PhD programs in France don't seem to get global recognition as the ones in the US or even some in the EU, with one or two exceptions.
It's the first time I hear this, I don't think this is true. There are many people who have done their PhD in France and have had a successful career abroad. I assume that this impression is based on international rankings, there are lots of reasons not to to take these rankings too seriously.
Even within France, PhD is condemned to belong to the academia and is rather ignored in the industry (if there's any).
This is a stereotype based on a tiny bit of truth: traditionally French industry had a tendency to favour Grandes Ecoles graduates, and consequently it wasn't necessarily worth doing a PhD for a career in industry because the income difference between PhD/non-PhD was not as high as in other countries. But it was never the case that somebody with a PhD in CS could not find an industry job! Additionally this discrepancy tends to disappear, especially with big multinational companies which compete for skills at the international level where a PhD is highly valued.
Could anyone familiar with the French system correct me on this? Is it possible/typical to research on a different topic from the one that I'm getting paid for, to change the PhD topic,
Be very careful about starting a PhD with the thought of doing another PhD, it's much better and safer to have the right topic and advisor from the start (that's true anywhere).
or even to quit the PhD in France?
Of course! Do you imagine that doing a PhD in France is like entering the Mafia, you can't leave alive? ;)
Historically some PhD contracts used to pretend that the money had to be paid back if the PhD student didn't finish in time. These were likely illegal contract terms, I never heard of anything like this being enforced (and I've known a good few people quitting their PhD).