Update!

I was able to pass without issues.

1. There was a sign placed right in front of the entrance towards the French customs booths advising that check-in facilities are closed in the French sector and bla bla, but one should not be deterred and proceed with joy.

2. The customs booths were empty.

3. After I passed the customs booths there was a chap with unclear authority, probably an airport employee asking to see boarding passes. Since I had boarding passes arriving in Geneva that day there was no issue. Enforcement seems lax: a man before me had picked up his parents arriving and was also let through because ok I'll make an exception for you mate. I do not see how he could force you to turn back but I guess he could call the constabulary.

Thank you to commenters for your help!