I've seen Framus Texans with nylon strings (on ebay, not a good guide to correct practice!). I'm not sure if all were. If yours is one such, it is not going to matter whether you check the neck relief (your test with a straight edge) with the strings on or off. If it's a steel strung guitar then quite likely the neck will be dead straight with no strings on, and the string tension will create the relief as strings are tightened.

Moo is right, there should be a slight forward relief, it's just the maths of the fact that when you fret the guitar, the string should leave every fret at the same angle, and the bridge is of course a bit above the level of the frets if they were in a straight line and it continued to the bridge. It isn't going to produce the difference you are citing.

Start by checking each string at the octave. It doesn't even matter if the string is all that in tune to start with. Play the octave as a harmonic. Now fret the octave. Are the two notes the same? Your tuner may help you decide.

If they are, then, allowing for the tiny difference caused by the stiffness and thickness of the strings as they cross the bridge and at the nut, (which is why bridges are angled, or even are made in two pieces like Takemine do, and why Buzz Felten nuts exist) the octave on the fretboard is indeed in the middle of the string.

DO it for every string.

If that is OK, then unless the fault is of an identical size at the nut and bridge (an unlikely coincidence) the problem is not the nut or bridge. It might be the actual fretting of the neck, but there are other possibilities.

If that is NOT ok, start by looking at the bridge. As I recollect the Texan has a classical style bridge, and it's possible that someone has lowered the plastic saddle so much that the wood in front of it is what the strings are bearing on. I reckon this would produce about the size of difference you seem to have. If so, or if the saddle is missing, put it back how it should be and if the action is now too high to play you have a different problem - probably (snce you say your neck is straight) a neck set or major distortion to the front of the guitar..   

If your guitar is a tailpiece one, then it's very likely that the saddle has been moved (if it is not stuck to the top). If you're lucky there may be a light patch on the front of the guitar to show you roughly where it ought to be. If the bridge will slide about, adjust it by ear or with the aid of the tuner until it comes right.

Check the nut visually. Are the slots all in good condition, or do they allow the strings to wiggle as they get to the fretboard? This is unlikely from your description as then the first fret would be very flat, the second fret less flat, and so on.

If the saddle seems to be in the right place (you can try measuring witha ruler as a first rough check) and the nut looks OK, change the strings. Strings do develop a taper after a while, but it's unusual for them all to do it at the same time.

If the above does not point to a cure, it may very well not be worth fixing it on a Framus - hang it on the wall as a collectable at best, and buy a modern, playable guitar: alternatively stick to root chords!