The case was detected several days ago in "a woman who is not pregnant," the minister told AFP during a visit to French Guiana, confirming information initially given by a medical source.
The couple lives in the Paris area, the minister's entourage said.
"She showed classic signs of the disease," an official said. "She was not hospitalised and is doing well."
Brazil has been the hardest hit country by the mosquito-borne virus, with 1.5 million cases of active Zika transmission.
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In nearly all Zika cases, symptoms are mild, resembling those of flu. However, the growing belief that Zika can also trigger microcephaly in babies born to mothers infected while pregnant has spread international alarm.
Microcephaly is a congenital condition that causes abnormally small heads and hampers brain development.
There is currently no cure or vaccine against the Zika virus.