Reader question: Are French state pensions and supplementary pensions (retraites des cadres) taxed at source or must I declare them?
Actually, both cases apply: you should declare your French pensions, even though they will already have had tax taken off at source.
The tax office will bear in mind the tax that has already been levied and will not charge it again.
Essentially, you declare your worldwide income (with some exceptions, such as income from tax-free French accounts) and then the tax office checks to see if you have already paid enough in at-source tax.
If you have, obviously nothing further will be payable.