Did your client relocate from the US to France in 2023?  Or did your client reside in both countries but spent in aggregate 8 months in the US and 4 months in France?

If he relocated from the US to France, did he travel to France for work while living in the US and vice versa?

Where was his employment based?  How was he paid?

Did his payroll in US and France include any component that relate to services performed in the other jurisdiction (e.g. bonus, deferred comp, options, etc.)?

Other than monetary compensation, was he provided any benefits-in-kind that may be taxed preferentially in France (but would not be so in the US)?

Did he participate in any nonqualified plans for US tax purposes (which is common among expats)?

"How do you determine the amount of FTC to be reported on Form 1116?"

That's a function of the France taxes he paid/accrued, his FEIE, and the limitations computed for the various baskets.

"Isn't it based on the tax rate stipulated on the tax treaty?"

Not for employment income.

It does not appear you understand the basics of international returns.  And there is a lot more than FTC when it comes to expats.  As you may be aware, penalties for failure to properly file various international returns could be substantial and would even toll the SOL in some cases.

I have no doubt you are a very competent tax professional in domestic issues but you may like to consider referring this client to an expat tax specialist.