Both of them will be required to file a federal return if they meet the threshold for gross income depending on their ages and marital status like anyone else. In addition, they may have an on-going filing requirement for state, depending on the state's rules for statutory and domicile residents.
You will also need to consider which country will have the first right to tax the different types of income and the extent to which taxes may be assessed by the country of source and resident under the relevant treaty articles based on various factors.
The husband may possibly claim to be a nonresident based on the DTA with France but that could have ramifications on his green card status and trigger expatriation.
Before they participate in any foreign pension plans, invest in foreign securities (such as ETF, mutual funds, REIT, RIC, etc.), or start any business overseas, they should carefully consider the potential US tax implications and compliance requirements. Unbeknownst to many who move overseas, thinking these are just part and parcel of global relocation that takes place everyday in this modern age, there are serious tax consequences that need to be contemplated and mitigated in advance.
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