Hi,
Just something that you should note is that a non tax resident individual is liable to income tax in Ireland on Irish source income (for example rent from an Irish property) AND Irish employment income where the duties are carried out in Ireland.
From what you have said I am assuming that you carry out your employment duties in Ireland and as such are therefore liable to income tax on that income in Ireland regardless of the fact that you are non tax resident.
I am not overly familiar with the French-Irish double taxation agreement, however, based on the general OECD model, as I understand it the DTA gives primary taxing rights in such a situation to the country where the employment is carried out.
PRSI is another story and something you should also consider. In the event that you are paying social insurance on the income in France, you will not have to pay PRSI here. However, given that the primary taxing rights lie in Ireland I would doubt this is the case.
Given the fact that there are a number of other issues from a tax perspective that should be considered when an individual comes to Ireland I would strongly suggest that you seek some advice.
Also on the midnight "cinderella" rule for determining residence, you should note that this is no longer relevant from 2009. FA 2009 now deems a day to count for determining residency if you are present at any time during the day.