Britline: Interest paid is tax free for French residents. It is the responsibility of non-residents to declare any interest earned to their local tax authorities.
and
Patrimea: What is the taxation of the livret A for a non-resident?
Booklet A is a totally tax-free investment. The remuneration of this investment, i.e. the interest received, is exempt from income tax and social levies. Thus, you do not have to include on your tax return in France the income received from your livret A.
However, it is not excluded, according to the tax treaties between France and the country of residence of the investment holder, that a tax is due on the interest collected in the so-called country of residence.