[Phonograph]

a franchise is just a way to group several products together
if you create one product, you don't need to make a franchise just for that

for example, the FF franchise has FF games
but rudra only has product since it's the one of its kind, so no need for a franchise

also, if you create a product that must be linked to a franchise, there is a "Link Title to this Franchise" > "Title ID" in the franchise edit option

if there was a "type-moon" franchise/company, linking fate, tsukihime and mahoyo would make sense
however, I don't think you can link mahoyo to fate franchise simply because there are some relations
if you check the wiki page of the game, you'll see it's not the fate series or any other fate relations (same for tsukihime)

as for princess witches, I don't see what franchise it could be, just let it as it is

edit: btw, you can't change a franchise into a product page, or reversely