Sorry, I know virtually nothing about the Canary Islands and Fuerteventrua (means strong winds in Spanish).
Closest I've been is the mainland in southern Spain and the Mistral winds were not blowing so I didn't get to sail.
I think that the conditions (unless it's calmer in the mornings or something) would be a bit overwhelming for a beginner/intermediate, and would be completely intimidating for you girlfriend.
I'm sure they have good schools there, and you can learn, but you can also be overwhelmed and give up the whole idea.
I'd look for somewhere warm with gentler conditions.
Bonaire in the Caribbean comes to mind as it's wonderful for beginners and pretty darn good for more advanced sailors with excellent instruction at all levels.
Hope this helps,