Yes the tube is not where any ID would be !! Its usually on the collar that attaches to the glass bottle !! Marcel Franck did not mark his items with that type MF !! I personally think this is just a copy-cat version of his atomizers !! There have been copies of designer items for the last 200 years !! There is one on the link I gave you that is quite similar to this but different mark !!

https://perfumeatomizers.blogspot.com/p/marcel-franck-marcel-franck-took-over.html

Scroll down here to see a similar atomizer !! Not sure it is the same but if it is ,, the name will be stamped on the metal collar !! Could also be a knock off of Marcel Franck

3rd pic

2nd pic

trying again, I couldnt see the picture on the other posts