There were no large native populations in the peninsula speaking what we'd call "French," though it's important to realize that that language was far from unified even in what is now called France. Norman French was different from Central (Parisian) French, which was different from the various Occitan languages in the south, etc. In fact, that continued to be the case into the modern era.

Post-Roman Latin in the west became the various modern Romance languages very, very slowly, with local populations' speech changing bit by bit and diverging from their neighbors'. So someone in Toulouse sounded different from someone in Bordeaux, but maybe mutually intelligible. Maybe they could also understand someone in Barcelona, but not as well. Someone in Toledo could likely understand at least pieces of the Barcelonan's speech, but very poorly of that of the guy from Toulouse. That's the general story of the Romance family, in a very rambly fashion.

So to directly answer your question: the various Romance languages spoken in modern Iberia were taking shape in the eleventh and twelfth centuries when the Reconquista was building steam. They certainly weren't speaking French, but medieval Ibero-Romance dialects hadn't yet diverged as drastically from one another as Portuguese, Galician, Castilian, and Catalan have today.

But those weren't the only languages spoken. Remember there were a great many Christians living under Muslim rule in the south of the peninsula. As a result, a fair number of them spoke Arabic (much like many influential English natives knew French in the Norman era). More of them, though, spoke Mozarabic, a divergent variety of Ibero-Romance that was heavily influenced by Arabic. And let's also not forget Basque, spoken mostly in the Kingdom of Navarre in the north!

I think I covered all the major languages (at least native ones, so not counting the various Italian languages spoken by merchant communities in trading ports). I apologize if things are poorly organized, I'm on my phone. Any further questions?