It is forbidden to pitch a tent (make a fire, fly a drone, let your dog loose...) in the federal free districts (from Fionnay to Chargeur), Louvie is located in the middle of a protected area. So no: it is not allowed to camp, or bivouac even next to the cabin.

Below is the map of the famous free districts:

https://www.bafu.admin.ch/bafu/fr/home/themes/biodiversite/infrastructure-ecologique/districts-francs-federaux.html

The nearest (and super nice) campsite is in Bonatchiesse:

https://www.bonatchiesse.ch/hebergementterraindecamping

So plan to go to Louvie during the day and not at night. Reaching Fionnay will take you 1.5 hours of walking. The Col de Louive is a 3-hour walk from the cabin.

Good hiking organization.