The criteria are described briefly on service-public.fr. As far as I can tell, your situation would not require you to register anything. It does not seem that there is a hard limit (under/over so many days). Staying more than 6 months per year would usually mean that you need to register your income but it's not clear if staying 6 months once does. Everything hinges on whether France is your “main home” and every description of this I can find includes some hedging like the “usually” in the previous sentence.
If you are liable, you will need to report your income. It's probably “easier” in France than elsewhere because, unlike any other EU country I know, France does not have a withholding/payroll tax system so that everybody needs to take care of this directly. This has to be done in the spring, for the preceding calendar year.
The date you arrive in France also matters inasmuch as some local taxes and the television license are paid by the person living in or owning a given property on January 1st. You don't have to do anything to take care of that, if you are liable, you will receive an “avis d'imposition” with the details. Incidentally, wealth tax is also calculated based on your assets on January 1st.
If it turns out that you are in fact considered a fiscal resident (or if you decide to move to France permanently), do beware: The first time around, you will have to pay all your income tax in August, for the whole year (after that you can pay in three times or arrange monthly prepayment).
Do take all this with a grain of salt as I am not a lawyer to begin with and this is an area of the law that I know even less than the rest.