How do they do that in France? My only solution would be to merge bikes and cars ahead of the roundabout which requires some caution especially from the car drivers.
I did explain one technique, where you basically have bikes enter the roundabout and "block" the inner lane as if they were a car, see here: https://news.ycombinator.com/item?id=41924222. I don't know if it's safer or not, but it is one technique that is legal in France since 2015, and an official recommendation to city planners.
Having a cursory look at Google Maps, I see four techniques: move the bike path completely away from the car road, force cyclists to dismount and behave like pedestrians (and use the zebras around the roundabout), allow cyclists to behave like cars and occupy the center lane(s), and the "bike path around the roundabout" technique.
I think both bike-path-around-the-roundabout and forcing cyclists to become pedestrians are equally terrible solutions. Moving the cycle paths away from roads is situational and doesn't really address the crux of the issue. I'll have to try and find more data/experience about the roundabouts that let bikes behave like cars and see how it is. Depending on the roundabout, that must be a harrowing experience.
I think building a pedestrian/cyclist bridge or tunnel could be a solid answer. Or maybe the other way around, because it's still mechanically easier for cars to go up an incline than for cyclists/pedestrians, at the cost of much, much more maintenance.