A person working in New York City must pay New York State income tax, United States federal income tax, New York City income tax, social security income tax, and medicare tax.
You cannot deduct anything for French children in France. You can deduct something for a child only if the child is a U.S. citizen, U.S. national, U.S. resident alien, or a resident of Canada or Mexico.
The entire amount of salary is subject to social security income tax and medicare tax. No deduction of any children is allowed. Those two taxes total 7.65%, so that is $7,650.
If only you pay U.S. taxes, then you take the salary, subtract $5700 for the "standard deduction" and ordinarily $3650 each for yourself and each child. $100,000 minus $5700 minus 3 times $3650 leaves $83,350. The federal income tax on that amount is approximately $17,300. So we are up to $25,000 so far. If you cannot deduct the children, then it would be approximately $90,650 after subtracting, $19,300 of U.S. federal income tax, and $27,000 total tax so far. If your spouse also pays U.S. taxes, then there is an option to file jointly, which may reduce the cost somewhat.
Figure roughly another $10,000 for New York City tax and New York State tax.
So we are up to a total of $35-40,000 total of all taxes, and $60-65,000 of after tax money that you could take back to France, if you did not have to spend it on living in New York.
Next, you get to pay any tax that France might charge, which would leave you with even less.