Yeah,
I've never seen a French bass with outer linings. I once saw a French bass with outer linings that were added by a shop in Germany because the original ribs had been so badly damaged by worms. 'Twas funny looking, to say the least.
The French models, of which there are a few distinct versions, are very clearly identifiable, if even only by the wood-choice. To me, the lining issue is a clear distinction, as is the size and shape of the blocks. While French purfling has been borrowed by a lot of other schools and the long French frog has been echoed in a few German and English basses, the inner-features like the blocks and cross-bars are unique to France.
Your Mittenwald bass is very nice. I've admired it before. It does have a very Tarr-looking outline. That very round model, in place of the longer, rectangular mold more commonly used in these basses calls a lot of attention to itself. Maybe it was a bass that Billy Tarr ordered and never received.