The 74 year old prisoner arrived at the complex in the Val de Marne department on 8 March and did not have any contact with other prisoners, according to prison authorities.
After the first symptoms of the virus were detected, the man was taken to Kremlin-Bicêtre hospital in Paris.
Justice minister Nicole Belloubet said on Friday that one of the nurses at Fresnes prison had also contracted the virus and was now in isolation at home.
France's health minister Olivier Véran announced on Friday that the death toll in France had risen to 79, with at least 800 new cases confirmed since Thursday evening, bringing the total confirmed cases to 3,661.
In a message published on social media, the minister also said that care should be taken concerning certain treatments.
"Taking anti-inflammatory medication such as ibuprofen or cortisone could exacerbate an existing infection," Véran wrote on Twitter.
"If you have a fever, take paracetemol. If you are already taking anti-inflammatory medication and you have any doubts, contact your doctor."
First case in French Senate
Elsewhere in France, the first case of coronavirus has been detected in the Senate.
Lozère senator Guylène Pantel, 56, was confirmed to have contracted the virus, according to a statement issued on Saturday.
Her entourage said that the senator is doing well and that she is not showing any symptoms.
"She was diagnosed because she had a slight fever, but it has now gone," said her spokesperson.
As French authorities step up measures to contain the spread of the virus, such as school closures, the presidency announced on Friday that the G7 will hold an extraordinary meeting via videoconference next week to bolster the international response to the coronavirus outbreak.
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