Catacombs

Buy ticket in advance to circumvent very very long lines.
Otherwise it can be a long wait more or less than an hour.
Allow 1 hour to visit the catacombs once you get inside.

It is not particularly tight ever, but once down there's only one way out.

If you are sticking to the path, there aren't any tight, narrow spaces. That said, I would definitely not take anyone claustrophobic down there as you are well below street level, there's no natural light, places along the route where it can be quite dark, and there aren't multiple exits to get out if your friend started to panic down there. I'd say plan to spend at least 60 to 90 minutes down there once you get through the entrance line. And you should note that you aren't going to exit the same place you enter, so if you are planning to meet up with your friend again after you finish, take into consideration you'll need to backtrack once you are above ground, or plan to meet them near the exit when you are finished.

Hi CM, my recommendation is to arrive an hour before opening and stand in line. We did that in September 2016 and it worked out great. There were about 600 people behind us when it opened. We were among the first to enter (they allow 200 in at a time). The self-guided tour takes about 45-60 minutes.

Depending on where you're staying, I'd figure travel time to get there, an hour to stand in line, another hour to see the catacombs, and travel time back. So about 3-4 hours total. I'm not familiar with the general area but it didn't look like there was much to do for that length of time. It would probably be easier to have your friend do another activity and meet you back at the hotel (or wherever).

PS - I'm not thrilled with small spaces myself but the catacombs didn't bother me at all. It is dark and damp and there are a number of (wet, slippery) steps. It's an experience!

The website states that people who might be claustrophobic should avoid visiting the Catacombes.

The stairway going down is one of those tightly-wound circular models, and there are places where it is completely dark. The overhead ceilings can be low, at times.
Mostly, there will be an oppressive lack of air down there - whether perceived or not - which is what might freak some people out, if they are not used to things like this.
If someone suffers from claustrophobia, I'd go visit the lovely Montparnasse cemetery, instead, while others go to the Catacombes.

Thanks everyone for your advice.