This is more or less my day job, though I work with academics.
There will almost certainly be some French taxes to pay, and the social security might be payable in France – this depends on a number of factors, including where you and your family are, and how long the role is expected to last.
Be aware that the tax system in France may or may not move to PAYE in 2019, so if the advisers don’t mention that, query how they expect it to work. (They may be assuming that it won’t be introduced at all, but make them spell it out!) If they think it’s coming in in 2018, ask where they got that from, as latest information is that it has been delayed.
Being a US citizen complicates things anyway…
PM me if you have any questions.