I have not read the French article but had a look at the review on Rational Wiki which seems to have done a good debunking job.
I speed read the Spanish article but have not watched the video. The author seems to set up some Aunt Sallies and make some dubious observations. The argument that Romance languages cannot be derived from Latin because they have a different typology does not hold much water. The history of many languages shows a drift from, say, synthetic to analytic.
No one has ever argued that any Romance language is a direct descendant of the language of Cicero. The emphasis has always been on descent from Vulgar Latin. The Romans did not conquer the whole of their empire in one go and different stages of Vulgar Latin would have been introduced at different times. Insisting that anything different from Classical Latin is not Latin is no more than an argument about precise labelling. Saying that Romance languages come from "Old Italian" is just to give Vulgar Latin another name. However, as touched on above, the possibility cannot be ruled out that some of the modern languages of Italy classified as Romance are to some degree descended from or influenced by non-Latin Italic langauges.
