I replied to ‘Boozer’ via a personal message (email via a mutual acquaintance) but here is what I said :
The 334 gearbox has the additional speed tacked onto the front of what is essentially a Type 328 three-speed box. This makes it longer. And to accommodate this the front chassis member (originally straight across) was redesigned with a bend in the middle to give a bit more space.
So if you wanted to put in a four-speed box you would need to cut out the existing chassis member and replace it with the newer version. Although I haven’t checked right through to 1992 I think the latter was then unchanged throughout, following the change to four-speed, so it might well be possible to get an aftermarket one from Melun or somebody.
But it sounds like a lot of work for not much benefit — I would guess that the gear ratio range in the 328 is similar to that in the 334 i.e. top speed probably would not be affected (although acceleration would).
One might also have to change the driveshafts as some had different splines on the inner joint.
You can see illustrations of the relevant bits in R4 Parts Book volume P.R. 808 pages 31.01 (328) and 31.03 (334), 50.04 (old chassis member) and 50.05 (new).
Incidentally ‘1970’ sounds a bit late for a three-speed vehicle. According to Album Renault 4 (Séjourné) the four-speed box came in in 1968. UK dealers might have had slow stock, of course.
Also, one should be aware that there is no synchromesh between 1st and 2nd gears on either the 328 or 334. Unless you double-declutch, changing from 1st to 2nd results in horrible graunching noises ( → possible damage to gearbox).
‘1968’ in the Séjourné book means the 1968 model year, which started in mid-1967. So Andy is correct in his date.