Can I go to Iceland with a valid French visa?

Yes, Iceland is a member of the Schengen Agreement, and you need a valid Schengen visa to go to Iceland. Once the applicant obtains a visa from any Schengen country, he can travel freely in all Schengen countries within the validity period of the visa. If the destination is more than one country, you should apply for a visa from the embassy of the destination country with the longest stay. If you stay in two countries for the same time, but enter Iceland first, you should apply for a Schengen visa from the Icelandic embassy.

Iceland is a Schengen country, not an EU country. Tax refund in Iceland cannot be handled in other countries. Tax rebates from other EU countries cannot be handled in Iceland.