One must remember that when Rome fell, the people in the provinces did not simply disappear. They, for the most part, stayed right where they were. The people of Gaul spoke a vulgar form of Latin, but it had become region specific, displacing much of the Celtic languages that were there before.
A linguist might be better suited to answer this question.
However, once Rome fell, the provinces were open for invasion. Here is where your tribes come in. Let's take, for example, the Franks. The Franks raided into Gaul even before Rome fell. Some of them stayed. Various people who were called Franks were some times enemies and some times allies of the Roman. When Rome fell there were Franks in the Roman army. Thus it can be assumed they spoke vulgar Latin, or something very similar.
Slowly the Franks gained control of much of Gaul and there developed Old French, which was based completely in Latin, thus a Romance language.
England did not have as long a period of assimilation with Rome. Rome was not as entrenched and so Latin did not become as wide spread. The same goes with Germany. If the average person did not speak it, it did not last.
Of course Latin remains an important language in England, as in the rest of Europe, partially because of its ties with the Catholic Church.