It doesn't on my '75....but it's a small clearance
Now I have the plastic housing type - not the chrome ones (I have no idea whether they came with the car or not.)
Those two 3/8" or 7/16" headed (IIRC) nuts or bolts (I just tightened mine last week too and I can't remember!) cna be reached through the various access holes in the door, although the window has to be in the right position near full down. I use a flexible shaft nut driver or a 1/4" drive extension that I have to first stick through the opening and then put a short socket on to reach at least one.
I was horrified the first time I got to it to see the mirror was actually a remote adjustable type, but the last owner had just wrapped the adjustment cables up and tie wrapped them rather than running them anywhere. Oddly, the passenger side is NOT an adjustable type - and that's the one you need a remote adjustment on! (They may be electric on the later C3's, I don't recall.)
On the mirror itself, the two bolts to the mounting stem tighten the mirror housings, but there is another central bolt from the upper stem to the actual mirror housing and I had to take the mirror off to tighten this one and stop the mirror wobbling around like a Corvette version of a Weeble....
Oh, one other thing. The gasket that the mirror mount mounts to the door through is handed! One of my mirrors had always been canted wrongly and I couldn't see how until I removed it and found out the gasket had been installed upside down. Once turned around, the mirror, for the first time since I owned the heap, pointed correctly. (Why they wouldn't just make the stem mount slightly different and use a symmetrical gasket is another "factory procedure mystery" to me....possibly they used the same mirror on different models with different angles on the door...)