A linguist named Mario Pei undertook a study of Romance languages to determine how far they had deviated from Latin. This is what he came up with. Lower scores means closer to Latin and higher scores means further from Latin:
Sardinian 8% Italian 12% Spanish 20% Romanian 23.5% Occitan 25% Portuguese 31% French 44%
I had always heard that Sardo was like Latin frozen in time. Italian is also said to be quite close to Latin still. In fact, it is from this land that Latin emerged in the first place. Spanish has deviated quite a bit, but I am not certain why that is. For one thing, quite a bit of Arabic has gone into Spanish. As far as other influences, I am not sure. There are influences from pre-Latin languages, but I am not sure how significant they are. The impact of Basque (which would be included under pre-Latin influences, is also not known, but it has effected Aragonese and Aranese.
Romanian has obviously been flooded with Slavic words.
Occitan is also different, but this is probably due to the French influence as Occitan is sort of a Spanish-French hybrid language like Catalan.
Portuguese is also very different, but I am not sure why that is. Clearly the Portuguese vowels have gone crazy, but why is that? Brazilian Portuguese had influence from Indian languages, but that did not affect European Portuguese.
French is the most different of all. The odd vowels appear to originate from a Celtic base (Gaulish). In addition, quite a bit of Germanic has gone in via the Franks and there was a strong Norse influence in the far north. Basque and Breton influences are not known. It is due to this strong differentiation that other Romance language speakers say that no one can understand the French.
