In localities with few/no roundabouts, the vast majority of accidents still happen at intersections. Intersections of roads are the most prone to accidents (for fairly obvious reasons), with or without roundabouts.
I believe there is research showing roundabouts are actually quite a bit safer in general, but it's possible it depends on various things. But anyway, accidents happen mostly where two roads intersect, either way.
Roundabouts make my bicycle commute way faster. This in The Netherlands where we cycle a lot. Difficulty or death is entirely incorrect. Suggest to compare the designs across countries, maybe there's a huge difference in the design?
It certainly seems to be a people problem rather than a roundabout deign issue from my experience?
People trying to "beat" people out onto the roundabout rather than giving way, people not using proper lane discipline and squeezing/cutting into other lanes etc..
Research shows the opposite. They can handle more traffic within a given timeframe. The bit about accidents seems strange. Not sure why you'd think that. I'm wondering if your roundabouts have some kind of design flaw.
Out in the countryside roundabouts in France operate in the "normal" way : approaching traffic yields to traffic already in the system, with the usual triangular "yield" sign making priority clear.
It's possible that your experience of French roundabouts is related to driver confusion between these two systems.