First, determine if the services are excluded by US-France treaty.

Your client's service sounds like it is considered "Dependent Personal Services" and under the US-France treaty, the first 183 days of income is excluded from US taxation ... however, that doesn't mean it can be ignored and not reported.

In general, US Citizens and US Residents must reported on their world-wide income. And they must pay US income taxes on their gross worldwide income, UNLESS the non-USA-source income is excluded or modified by tax treaty. [IRC §61(a)]. File form 8833 to exclude that treaty based modification and attach to their 1040.

If Client pays tax to a non-USA country on non-USA-sourced income, Client can sometimes reduce or eliminate their US income tax by (1) Foreign Income Exclusion or (2) Foreign Tax Credit. These 2 method may cause different results, so do the math to get the best result.

Next, if services and income are not excluded by tax treaty, you must determine their "residency" (this has nothing to do with citizenship).

RESIDENCY - In general, is the location (tax locality) of their permanent home or principal place of abode:

PART YEAR RESIDENT: Generally, you are a part-year resident if you moved to or from a tax locality during the tax year with the intention of establishing a permanent residence in your new tax locality and not currently returning to your prior residency..

NON-RESIDENT: Generally, you are a nonresident if you do not have a permanent home in a tax locality at any time throughout the tax year. e.g.. you intend to return to your prior residency.

DUEL STATUS CITIZENS (this can happen in the year of arrival & yr of departure as a “resident”)-

If they are Green Card holder (Resident Alien), they file 1040. If they have given up, lost  or never had their Green Card status (Non-Resident Alien), they file 1040NR and 8833.

There may be restrictions on filing MFJ in some cases so review thoroughly the IRS publications on this topic. 

The FBAR-114 may be required if foreign holdings exceed $10,000 and on their Form 1040, Form 8938 is used to report client’s accounts, holdings and income.

IF THIS ANSWERS YOU QESTION, PLEASE MARK IS "SOLVED"