Technically you are correct in saying she "officially" is a frigate. The French Navy has a somewhat ambiguous approach. They designate the ships first and second rank frigates but they assign a hull classification of a destroyer the first rank vessels, and frigate for the second class. Forbin is a joint destroyer project and the class is designated as a destroyer by the other participants. Janes's also classifies them as destroyers so it all boils down semantics.

Impressive ships nevertheless :-)