I've worked on some classic arch-top floating tailpiece guitars before, and I recall the strings were close, but still able to reach enough to wind on the posts.
Some string manufacturers may have slightly different lengths, which would take some searching on the manufacturer's web sites for info.
There are some custom string manufacturers as well, that will make string sets to order, including length. You will pay a premium price for them though.
Another option would be to use a set of Baritone Guitar strings, which are made longer for the longer scale length. You would probably have to replace the high E string with a single to make up for the thicker gauges the sets come with.
Some of the "Gypsy Jazz" guitar sets may be longer for the arch tops also.
EDIT: (cleaning up multiple edits:)
12 string guitar sets may work also, some will be as long as 43 inches
Looking at some of the Framus history sites, that may not be an original tail-piece; in the picture it looks a little shorter than some of the stock pictures. I have seen that style of tailpiece in a couple of different lengths on vintage instruments.
You might consider putting a longer tail-piece on.
From what I've found, the dimensions of the guitar are a 24 inch scale length, with a total length of the guitar at 37.5 inches. Product recommendations are off topic for this site, but searching for a manufacturer's name and "string length" will usually get you results. For example, D'Addario strings come in at 39 inches, which should be just long enough to start at the furthest pegs.
One of that guitar model I saw for sale is listed as having a D'Addario Phosphor Bronze set installed, so apparently that is long enough.
You can start the strings in the plain steel portion, you do not have to get all the way into the winding. The main strength of the string is the core, and it should hold the tension even if you don't get winding onto the post, so the strings may seem too short, but will still work if you have enough length to get them started.
Inserting from my comment: Looking at the headstock, the shape looks different than other examples of the stock guitars I've found pictures of. So far it looks like the stock headstocks had a curved top, or narrow square shoulders in one example. The headstock on yours is wide at the top and looks like it has some carving coming into the pegs starting at the nut. I also haven't seen any examples that don't have a truss rod slot in the headstock.
One of the problems these old archtops (Kay included) have is a tendency to have neck problems, either with the action getting too high to use, or warping.
It may be that you have a neck replacement and a longer scale length was used, adding to the overall length of the guitar.
You can measure from the nut to the 12th fret, and double that number to get the scale length. The stock length should be at 24 inches. If it is bigger than that, you may have a different scale length neck installed. Because the bridge is floating, you should be able to compensate if this is the case, once you find strings that fit.