It might be worth mentioning that the Livret A is subject to 30% tax for non residents. The 30% tax is not deposit interest tax but rather a different tax type. Hence, it seems to not be deductible against your Irish DIRT liability.
@Lightning. I can't find a reference anywhere to Livret A being taxed in the case of Non Residents. When I was researching it, I found a lot of this kind on language floating around:
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.
Which could be said to be slightly misleading, but it definitely doesn't say that it will be taxed in France. As an Irish tax resident I fully accept that it will be liable to DIRT in Ireland.