Hmm, in for a penny.....
1. On the backbore issue, I'll go out on a limb, and say you have plenty of steel in the barrel for a backbore. Why do I say that? 'Cause I've never seen one that didn't. My own pride and joy R10 12 gauge had a massive backbore done at some point in it's life, and no less than .060 of steel remains at any given point. Closer to .090 at quite a few spots in the barrels. The guy who does the backbore will tell you if the facts are otherwise, and, be sure to get back and tell me if I was full of poo, but, I'm pretty sure I'm not. French proof is pretty potent, and they usually left quite a bit of steel in those tubes.
2. How much choke you want? Jug choke it, or screw choke it. You will win the choke lottery either way. Someone here (likely someone who has never owned a Darne, and wouldn't say anything good about one, in any event) will be along to tell you to never put screw chokes in a double shotgun. Screw them. It's your gun.
3. Depends what's wrong with it, BUT, a Darne R model safety is pretty much child's play in terms of a gunsmithing repair project-there isn't much there, and it is a straightforward design with few parts. No big deal, even if the 'smith has to make some new parts.
4. Remember when I said "In for a penny...." up above? Welcome to the world of double guns and gunsmith's. Do not forget this thought-you get what you pay for, either in guns or gunsmithing, when it comes to double guns. Your local Remington 870 wrench won't be of much assistance with a Darne and SHOULD NOT be trusted with your old French gun.
Kirk Merrington is an English trained barrel maker, and can provide you with the services you require on this gun. Google him. He likes steak and shrimp as much as you and I do, doesn't come cheap, and shouldn't. His skill set took half a lifetime to develop.
The good news is, a Darne isn't a maintenance pig, excepting perhaps, wood work, and once he goes through it, your done, pretty much, for this lifetime. Getting back to the wood, don't try to alter it, excepting LOP, as the attachment to the gun is somewhat complicated, and the Achilles heel of the design.
Good luck. For me, for many years, a Darne has proven to be a wonderful rough shooting gun, perhaps without peer, for what I do and how I do it. A 16 Darne is about as well balanced, lightweight and durable combination of bird gun as you are likely to find.

Best,
Ted