Paris, will timed entrances be needed for main sites with museum pass?

For the Degas exhibit at the Orsay, you do not need any additional ticket other than your pass. When you approach the Orsay, be sure to look for entrance C which is to the far right as you are looking at the front of the building.

There is still often a long line at Ste Chapelle due to the security line. I don’t know about the Arc de Triomphe.

Timed entrances are not available for most museums in Paris. The one exception is the Louvre which is now requiring them. You cannot buy them for the Orsay, Orangerie, Arc du Triomphe, Pompidou, Invalides etc. for the Louvre you can buy them with a Museum Pass. In summer you can buy them for Versailles but not with a museum pass -- with the pass you need to stand in the main long long long security line and thus should arrive no later than 8:30 if you don't have a timed ticket. I don't think they sell timed tickets after November 1, but check the official web site -- we could not get them for June 1 and so bought Kings Apartment Tour tickets to bypass the line and then a week or so before our visit, the timed tickets were again available.

We have been to many special exhibits at the Musee d'Orsay and never had a line to enter the exhibit. Always have pass or ticket ahead for the museum itself which often has very long lines if you don't. Maybe someone who has done the Degas will chime in with their experience -- certainly possible that there could be a line, we just haven't experienced it with their special exhibits, but Degas may be a particular draw. (they have really great special exhibits)

For special exhibits at the Grand Palais or Villette, even with a timed tickets the lines can be long. We waited over half an hour to enter the Russia exhibit at the Grand Palais last spring with our timed entry and it was more like 45 minutes with timed entrance for our King Tut exhibit at Villette. When we went to the Vermeer at the Louvre, we got in the exhibit line a half hour before our entry time; it took 45 minutes to get to the ticket taker and then another 45 minutes after that to get into the exhibit itself. One elderly woman who couldn't stand that long collapsed and was carried out on a stretcher. I don't know if the Da Vinci exhibit is being better managed but given the Louvre's recent dismal track record I doubt it.

I visited d'Orsay twice last month and neither time was there a line at the Degas at the Opera exhibition. I actually took a look at the line 4 times - twice each visit. I did visit the exhibition on my first visit. It was more crowded than you'd imagine from no line. It was also hot in there - not much air circulation, but that is a normal complaint for me, lol! I also went by d'Orsay 3 other times on Tuesdays and the line to enter Door C with the Museum Pass was hours long. On other days there was a pretty short line. I'd avoid d'Orsay on a Tuesday (when the Louvre is closed) if you can.

In d'Orsay be sure to see the new Post Impressionist galleries (Van Gogh, Gauguin) on the 5th floor. I was looking for them but did not feel they were well-signed to find the entrance to the galleries which are across the front of the museum kind of over the front doors.

I just happened to be walking by Sainte-Chapelle one morning when there was absolutely NO line so I popped in because I had the Museum Pass. If you happen to be in the area definitely go by here even if it's not on your plan for the day! You might catch it at an ebb.

The Louvre sadly is imposing timed tickets, with a Museum Pass in theory there is no problem, in practice, if it is a very busy day, Museum Pass holders have been refused entry...
But if you visit in winter, avoiding Christmas, that should not be a problem.

I was at St Chapelle on a Sat mid Oct last month when they opened. There was no line and we got right through.