By the way, a Lingua Franca is a shared language that's used by speakers of different languages so they can communicate with each other. That's not the same thing as Latin changing into different languages e.g. French and Spanish. So you should clarify which question you mean.

There's some previously answered questions as to the second question, and perhaps the first, in the FAQ.

Related question: When did Latin stop being used as a trans-European standard language? Is this related to the decline of the Catholic church?

I believe the Treaty of Westphalia after the Thirty Years' war was the first international Treaty which was not written in Latin but French. It is my understanding that it is from this Treaty (1648) that French became the de facto international language.

Whether it's true or not, I had an Italian tell me that Dante's writings were full of unique alterations of Latin and because his works were very popular at the time, this set the stage for a modification of Latin into Italian.