Intra-Schengen travel in April 2021

Right now, the whole of mainland France is under lockdown. Crossing provincial borders (département) is only allowed for limited purposes and nobody is supposed to travel anywhere for leisure (that's irrespective of citizenship or status). Restaurants, museums, and many shops are also closed.

Since you are already in the Schengen area, most of the formal restrictions on travel from outside the EU do not apply to you and crossing the border is technically not forbidden in itself (after a PCR test) but after that you are supposed to stay put and tourism is not a valid reason to go out of your chosen place of residence.

France is also one of the worse affected countries in the EU so you would run the risk of additional restrictions on entry to Italy or Iceland being imposed while you are there.

In terms of visa, it shouldn't be an issue as long as the visa is valid (and ideally that the "main purpose" of your travel remains in the country which issued the visa), though expect passport/visa checks while travelling between Greece and France, contrary to normal Schengen rules.

However, in terms of the ever-changing Covid restrictions:

• France is currently under lockdown. All bars, restaurants, museums, malls, non-essential shops, etc. are closed.

• You are not allowed to travel within France.

• You need to have a PCR test less than 72 hours old

• You need to present a signed declaration

I believe Iceland is no longer under lockdown, but they do have a quarantine regime in place. Italy is in lockdown.

Basically, definitely not the right time to do sightseeing...