It is my understanding (and please correct me if I am wrong) that…
Latin remained the most important written language in southern Europe well past the end of the 1st millennium AD.
By 1000 AD, languages that we can identify with Italian and Spanish were already the commonly spoken languages in the Italian and Iberian peninsulas. They were about as different from each other then as they are now.
Even by 400 AD, written Latin was quite different from the Vulgar Latin that people were actually speaking, when relaxed at home with their braces off. But at that stage, the various regional Vulgar Latins were still basically mutually intelligible.
Is this correct? Is there good evidence or reasonable opinion about when “Latin” stopped being the real native tongue of the peoples of those regions?