Solène was historically a male name in France, as it was the name of Saint Solène (sometimes also written as Solenne): he was bishop of Chartres (France) in the 5th century AD. Nowadays, though, the name is predominantly female. But because it was a legitimate male name in older times, this name should be classified as unisex.
I'm loving this name right now, don't really like the meaning "solemn" but it doesn't really matter to me. It actually reminds me of the sun because of the "sol" part. At first I thought it was pronounced sol-een and thought it was okay but "so-lenn" sounds amazingly beautiful.