Couples can have different fiscal residency

Fiscal residency is determined individually and it is possible - though not usual - for one partner in a couple to be a fiscal resident of France and not the other.

In this case, typically, it would be necessary to make a joint declaration in which you declare all the worldwide income of the French-resident partner and the French-sourced income of the other.

One exception to this is where a married or pacsed couple has a séparation de biens matrimonial regime and are formally separated (but not divorced). 

Note that most British marriages are considered to fall under séparation de biens (see: tinyurl.com/which-regime for more about how foreign marriages are categorised). This is also the case for many, but not all, US marriages. 

This is where each partner keeps ownership of their own goods that were purchased by them or gifted, or bequeathed to them. In this case each partner should make separate declarations, in the case of the non-resident to the non-residents’ tax office at Noisy-le-Grand.

Note, however, that a couple’s marriage regime in some cases changes after 10 years in France or after the couple take French citizenship. 

There can be other exceptions to the joint declaration rule and it is best to check with the French residents tax office for clarification about how you should declare with regard to your respective living situations and your kind of matrimonial regime.

See the link above for more about regimes. With regard to a pacs the regime is séparation des biens unless you expressly opted for the alternative indivision (ownership in common) regime.