Yes, you would go into a HBB from this seat. HBB is the last seat type that they need. I would keep her in her current seat for a lot longer, though. You'll get another year out of it easily, maybe a year and a half. The limits on it are 105cm and 19kg - it's not the end of the world if you get to say 106/107cm and then suddenly realise. As long as her shoulders still fit under the headrest, it's not unsafe to use the seat.
You get the best safety if you can move straight to a HBB so the seat is only doing one job, but if you're really keen to move away from the spin now, you could look at Maxi Cosi Titan i-size (all the i-size variants are good) or Britax Evolvafix, Advansafix or Versafix (depending on which model is most easily available in France.) Those seats would allow her to stay in a 5-point harness which is then removed later on. They need top tether to fit them for the harness stage. I would prefer these seats to the Joie Bold, which you might be recommended (but which isn't available in France anyway).
There are also rear facing seats which go up to 125cm/25+kg if that is something you are interested in?
As a minimum she should be at least 100cm and 15kg to move to a HBB with seatbelt. It's better if you can get her to 105cm before moving, though. There is some evidence from the US that physical body size makes a difference to safety here. A lot of shop asssistants in France will tell you that from 100cm and 3 years, it's fine, but that's not really up to date or reflected in the evidence.
Whenever you're ready to move her, since this seat should last her longer than any other seat you've had and she's old enough to tell you what it's like, I would recommend going to a large baby goods store and trying different seats out to see what kind of a fit she gets, and how comfy she finds them. Whether you do this now with one of the harnessed ones (and for these I would only look at Maxi Cosi or Britax - the safety is too variable on other brands, even Bébéconfort) or wait until she is closer to the limit and then go to look at high back boosters, it's worth doing.
Once they go into HBB they can do their own seatbelt, or you can do it. If you want her to do this I would recommend also checking the fit in the car - it's easier to reach some buckles than others based on the shape of the chair and the base. You might also want to check how it fits against the seat as she grows and you move the headrest up. If your car headrest is interfering, you can usually turn it backwards or take it off.
Lots of brands are good for HBB but the usual are good quality - Joie, Nuna, Britax, Maxi Cosi, Cybex, Recaro.