if you are referring to the single shot, break action Baikal, then no problem. A friend of mine owns one in .222 and had the trigger worked on by a local smith who did an beautiful job and reported no problems. I understand it was quite straightforward. Dave has used his .222 on deer and I have only shot it on the range, it is amazingly accurate. Fitting it with a Vaime type moderator should again be a simple job for a smith, the only problem being the overall length and therefore balance when the moderator is fitted. For the cost involved for such a specialised piece, I'd be tempted to shorten the barrel prior to fitting the moderator and go with the Baikal. Another friend of mine had a BRNO Fox in .222 and had ongoing problems with wandering zero and poor stock fit and inletting. May have been a one-off but he ditched the rifle, bitterly disappointed.
Are Tikka rifles available in France? They make a beautiful .222. I have never shot ANY Tikka rifle that did not produce jaw dropping accuracy out of the box. Superb rifles and mid-priced. I have one in .243 and would not trade it for the world.