Stripped thread on steerer. Who is at fault - me or LBS? Background
I ride a Peugeot PKN10 (1980 or 1979 I'm unsure of the exact date).  Three months ago I had a cracked chainstay replaced at my LBS.  This required removal of the original fork and headset so the frame could be clamped and welded.
When rebuilding the bike the LBS recommended that I replace the original headset (a vintage Lightrace model I believe to be this one) with a modern headset, advice which I took on the basis of their expertise.  The listing for the linked item notes that the Lightrace headset is French threaded.
The Issue
The new headset the LBS fitted was (what I know know to be a British threaded) Tange Passage.  I was told this might loosen after a bit of riding and if so to return to the shop for an adjustment.  When I got the bike home I noticed the top adjustable race was so loose it could be turned with my fingers.  I returned to the bike shop for an adjustment, which tightened everything up.
I then rode the bike for 2 months. After around a month the top race of the headset was noticeably loose again, and I made the adjustments myself (as it was not convenient to return to the LBS).  My daily ride is approximately 5 miles, in heavy traffic in a busy city - as such I couldn't hear or particularly feel grinding in the headset.
On a longer ride in the countryside (approx 25 miles on country lanes) this became very clear though - after 5/6 miles the headset became so loose I could turn it with my fingers again and I rode very cautiously to my destination and back again (there was no opportunity to 'turn back' and resolve the issue when I noticed it).
It was clear at this point that the issue lay with the headset slipping on the thread of the steerer. Immediately after the countryside ride I removed the headset and fork off the bike completely.  The thread of the steerer is clearly stripped, as well as the inner thread of the locknut.  The LBS has advised that both now need to be replaced.
The Question
After seeing the steerer and doing my own research online I believe the LBS fitted the incorrect thread of headset (they are currently checking to see whethet this is the case - I will update when I have a definitive answer). My conclusion is that an incorrect headset was the root cause of the damage.  The LBS has said that I should have come in sooner if I noticed the headset was loose and not ridden the bike for 2 months - they believe I have caused the damage by not acting on the signals earlier.  The LBS has not brought it up, but there is of course the matter of the adjustments I made myself - possibly these caused irreversible damage to the steerer.
My assumption was that the bike shop would diagnose the correct thread type of the steerer and fit the correct part, and as such I when adjusted the headset I was doing so on the basis that it had been correctly installed and therefore could be easily adjusted without damaging the steerer.  Equally, doubt I had as a result of noticing the headset loosening on a number of occasions was counteracted by trust in the LBS - my assumption was the bike was fine to ride as the initial work had been completed by professionals.
Between a new fork, a new headset and labour (£80 + £20 + £15 = £115) this has become costly to resolve.  It's also notable that I have already payed £35 for the (arguably unnecessary) Tange headset and the labour to install it.
My questions here are threefold:

Can installing an English threaded headset on a French threaded steerer cause this type of damage?
Who does the fault lie with here - me or the LBS? Who should bear the cost of the resolution?
If the resolution is to meet in the middle (registering responsibility to both parties), what is a fair way to split the financial cost between myself and the LBS.
Absolutely.
If they actually put anything but a French headset on a French fork, it should be 100% on them.
Hopefully they will fess up and cover the whole thing.


Just to be clear, measuring the difference between a French fork and the more common ISO/British is super easy. The OD of a French steerer is 25mm, and common 1" is 25.4. The thread pitch is also different. The parts just don't fit right together. Making this mistake and sending it out the door without noticing anything amiss is implausible.

Also, if you did have a French fork and it's being replaced with ISO, they owe you a new stem too because the quill OD/steerer ID is .2mm less on French than ISO.