Hi and welcome to the forum.

The question of your "tax residence" will probably depend upon where you are the rest of the year. Under the French tax Code (Article 4B, if you're interested) you are deemed to be resident in France for tax purposes if:
- you have your home or main abode in France or
- you carry on a professional activity in France, whether as an employee or not, unless you prove that this activity is carried on in France incidentally or
- your centre of economic interest lies in France.

The terms are deliberately vague, as most countries take the position that you have to be tax resident somewhere. If you are determined to be tax resident in France, then your worldwide income will be subject to French income tax.

The six months or 183 day limit is only a guideline in most countries. I don't think it's written into the law most places. If you have four different homes around the world, you may wind up "tax resident" in the one where you spend the most time, or that you use to receive your bank statements.
Cheers,
Bev