Headset: take the top nut from the Bertin fork and see if it will thread onto a British thread fork. If it does, a former owner used an incorrect headset on your Bertin. That would help to explain the thread damage at the top of the steerer tube. Also makes the damage potentially less awful than you might at first have thought. The French standard is a smaller diameter. The British threaded headsets will thread on to the French steerer, very loose fit, and it is a bad idea. Folks do it anyway.

Juvela's idea to float some brass and rethread the existing steerer gets even more appealing if you determine that the removed headset was oversize = British.

Seatpost: is the stuck post made of aluminum or carbon composite? I cannot tell from the photo. Patience will be your friend in releasing the stuck seat post. There are methods more appropriate to aluminum than to carbon, hence the question. You might measure its diameter to get a sense of how much too large the post is for the frame tube.

Compare your Bertin frame to this one:

1970's Bertin C 132? - 61cm - A worthy save (of course!)?

which has a round Durifort decal at the top of its seat tube. Its Campagnolo 1010-1 rear drop out looks similar to yours.

Your seat tube top most decal shadow does more closely resemble a rectangular Reynolds one.

It is fun to examine the variations.