There's an interesting discussion about this topic at this link (in french). Personally, I think you might be better (a) to find out whether there is a Livebox setting that can be changed; or (b) move to a different provider (when you can get out of the Orange contract).
Let's start with option (a): There may still be an option in the Livebox settings to keep a connection permanently up or drop it after (say) 15 mins. of inactivity. If this option is still there, try changing it to the other way round. (This option was around before the bl**dy Liveboxes came onto the scene. The early versions of those were a complete heap of ordure but the modern ones are better, though the early versions were so bad that almost a pile of wet string would have been an improvement! You should be able to get some help by queuing up in your local Orange office or by asking Orange's English help-line (09 69 36 39 00, I believe). Unless you're very technically capable, I'd avoid even thinking about a non-Orange VOIP route. Telcos, such as Orange, typically set up the lines to users so that there are separate 'virtual circuits' (VCs) for voice, data, & TV, setting appropriate priorities for the different functions. Unless you're able to make use of the VCs in the way that Orange does, you will not get the prioritization that voice traffic needs nor will you get the free calls that you're already paying for. Sure, a PAP2T device would give you VOIP capability, but no-one said that it would give you decent sound quality. For that, other issues, including network prioritization, come into play.
Another possibility, noting that you have said elsewhere that you have a very fast connection, might be to see if you can opt for a slower but more stable speed. This is an option available in SFR boxes, but I don't know if or how it could be done in a Livebox.
Option (b): For many years, until I got a fibre connection, I got pretty good service from a SFR/Neufbox. People I support still have them and they work solidly 99.9% of the time. Other people I know have Free boxes and quite a few have Liveboxes. The latter don't appear to have your problem, which is why I'm thinking that you might just need to configure it differently. Nevertheless, you should certainly be considering alternative suppliers if you can't get this resolved.