The CX is a very good all-round bike. It's been very popular for that reason with couriers in GB. I am on my third one now. Number two went around India and overland to Europe two up towing a one-wheel trailer. They are still very popular in Germany where 20,000 are said to be still registered. Parts are no problem. You should be able to pick one up in France for a song, as the French can't seem to be able to give them away.
I find it a very comfy bike and passengers have commented that they find it more so than many BMW.
Reliability is a mixed bag: many just seem to keep going without any major work. Others experience catastrophic engine failures (normally big ends). I don't know why, but suspect that some people thrash them when cold. The engine can take 20-30km in Winter to get really warm.
My long-distance bike experienced numerous ignition and charge coil failures. In the 165-odd K that I owned it the engine was out about every 10,000k (no kidding!). However, this was partly due to my conversion to the automatic cam chain tensioner, which has several design faults, as I found out afterwards. (I have a document on how to fix this.)
The cam chain is another weak point, if it's not adjusted often; I recommend every 3000k.
When the time comes to buy one you should arm yourself with a new oil filter and watch out for these then:
Engine rattles: check the fan first. If it's loose it needs to be replaced, no big deal. If not, it could be the cam chain. Still no really big deal, except the engine comes out. What you really don't want to hear, though, is a rattle that turns into a knocking noise when give it a bit of throttle. In any case, before ever making an offer, remove the oil filter and bend the paper "fins" apart. (The filter gets destroyed in the process; that's what you bought the new one for.) Gold coloured metal flakes in the bottom indicate a bearing about to fail. Count on a major engine overhaul. I have pulled several such engines apart and in most cases the crank was already damaged.
Check the battery gets charged.
Finally, remove the rear wheel (I'm serious). Inspect the splines between the hub and the final drive. Normally, they should be covered in MoS2 grease. If these are allowed to become dry (and rusty) they wear at a frightening rate. When new the teeth and the gaps between them are about equally wide. The teeth on the drive should be about two thirds still there. If not count on replacing the drive! The sleeve on the hub can be replaced, but not the crown wheel.
The original shocks are very soft, too soft for two up.
These are all the CX specifics I can think of. You still need to check all the other usual items...
Cared-for CXs can reach very high mileages. Oil consumption is normally near zero. In summary: very recommended. I only wish I'd had a CX650! Heaps more torque.
Another, similar Honda you may want to consider is the NTV 650. I've heard lots of good things about it, but have never ridden one.
Salut from Southern France, the bikers' paradise,