The hunger strike, which began last week, is in support of Iosu Uribetxebarria, who was convicted of kidnapping a prison official in the 1990 and who wants to be released on parole because he has cancer.
He has been transferred to a hospital in the Basque city of San Sebastian in northern Spain and has started refusing food and medical tests related to his cancer.
In Spain, the authorities said Tuesday, more than 100 prisoners were on hunger strike in solidarity.
The French prison administration did not specify how many prisoners are taking part but said that 15 prisons are concerned.
The Eta prisoners' association, Herrira, claimed that 91 inmates in 23 French prisons were on hunger strike as of Monday and added that they had added a call for the release of 14 other terminally ill prisoners in Spain to their demands.
Some 600 Eta members are in jail in Spain and about 100 in France.
Eta is blamed for more than 800 deaths in a four-decade struggle for independence for the Basque country in northern Spain and south-west France.
In October 2011 it announced the definitive end of armed action, following the announcement of a permanent ceasefire in January of that year.