How does language transfer occur from French to English within native french speakers' mind? Can we observe this phenomenon ?
L2 acquisition is studied, and there are many theories which attempt to explain how the L2 is acquired. If this question is for a class you would have to consider what the material is saying to properly answer the question.
Otherwise, the basic way that L2 acquisition differs from L1 acquisition is that L2 acquisition is a generally conscious process (using metalinguistics awareness), the level of ultimate attainment will be less and less perfect as the learner ages, the L1 will influence the L2 permanently, this is known as fossilization, and the time which it will take to learn will differ from user to user unlike L1 acquisition which tends to be on a fairly fixed schedule.
L2 acquisition will hypothetically be structured in such a way that starts with the individual's initial hypotheses (what the person unconsciously thinks about the task) that the L2 is structured like the L1. The L2 code (grammar) will be built from the L2 in such a way that bit by bit the rules of the L1 are modified to accommodate this new language.
Simultaneously bilinguals seem to be neurologically structured like bilinguals, suggesting that two independent codes are constructed using the UG during the critical learning period (using the LAD), this does not seem to be the case for later L2 learners. For later L2 learners the L2 code seems to be relatively dependent on the L1 code.
Actually, L2 acquisition from French to English is studied a lot here (Montreal). My psycholinguistics teacher studies L2 acquisition. I could ask him if I did not properly answer your question.
It's important to know that like jlawler pointed out, we cannot observe the mind, we only have various (and conflicting) theories positing and predicting underlying cognitive structures and processes.