The Ufap-Unsa union said that new propositions from Justice Minister Nicole Belloubet were the "basis for a profound evolution in our prison system" and it would agree to end the protests.
However two other smaller unions, the hard-left CGT and FO, rejected the measures announced by Belloubet which include new equipment to manage Islamic extremists behind bars, including maximum security cells, as well as the creation of 1,100 new prison jobs.
The justice minister also announced a package worth 30 million euros in extra pay for guards who have faced a series of attacks from violent prisoners in recent weeks, which have been widely reported in France.
The action by the guards, the most significant in two decades, was the first major industrial dispute faced by the government under President Emmanuel Macron since his election in May last year.
Belloubet told Europe 1 radio on Friday that government was making "very serious offers", while calling for "a sense of responsibility, an appreciation of the situation."
France's prisons administration said 116 of the country's 188 jails were affected by the protests on Thursday, with guards at 42 facilities refusing to show up for all or part of their shifts.
Only about 60 prisons experienced work stoppages early Friday.
Conditions in French prisons have long been a source of anger among prisoners and guards, and an embarrassment for the state, with Macron once describing them as "disgraceful".
Adding to the guards' grievances is the radicalisation of inmates who come under the sway of jailed Islamist extremists and jihadists.
French prisons have developed a reputation for being hotbeds of radical Islam that have turned out some of the jihadists behind a series of bloody attacks in recent years.
The protests began after a convicted Al-Qaeda extremist attacked guards at a high-security facility in the north of the country on January 11th with a razor blade and scissors, injuring three of them.
A series of other assaults occurred shortly afterwards, often by radicalised inmates.
"These people go to work every day, civil servants, fearing for their security or their lives. We need solutions which respond to this concern for working in safety," Laurent Berger, head of the national CFDT union which does not have a chapter for prison guards, said Friday.