For any stay in France exceeding 90 days, you are required to apply in advance for a long-stay vis. In this instance your nationality does not exempt you from requirements.
Whatever the duration of your planned stay, the duration of your long-stay visa must be between three months and one year. In order to extend your stay beyond the period of validity of your visa, you must apply for a residence permit at a prefecture.
During its period of validity, the long-stay visa is equivalent to a Schengen visa, enabling you to move around and stay in the Schengen Area outside France for periods not exceeding 90 days over any period of 180 consecutive days, under the same conditions as if you held a Schengen visa.