The attacks come as French officials test a range of preventive measures after a string of jihadist attacks over the past two years that have left more than 240 people dead.
Some of those responsible were involved in Islamist networks in jail. They include Cherif Kouachi, one of the gunmen who attacked satirical magazine
Charlie Hebdo in January 2015, and his friend Amedy Coulibaly, who killed four at a Jewish supermarket two days later.
Dealing with radicalised prisoners and stopping them from converting fellow inmates has been a priority, but the results so far have been mixed.
"De-radicalisation efforts were set up very quickly, and there are lots of gaps," said Esther Benbassa, a senator who recently led a commission on the issue.
In the latest prison attacks, a convict at the Mont-de-Marsan prison in southwest France attacked guards on Monday as he resisted a search when his
gym bag set off a metal detector.
Seven guards were hurt, including a woman with a fractured sternum and a man with a broken nose, Ludovic Motheron, a CGT union official at the prison, told AFP.
The justice ministry said the inmate had not been jailed on terror charges but had nonetheless been under surveillance for "radicalisation," though a source close to the inquiry later said this was largely due to his history of violence.
Another inmate at a jail in Tarascon, the south of France, who was described as radicalised left another prison guard in hospital on Tuesday after punching them several times.
These attacks came four days after a German convict linked to Al-Qaeda, Christian Ganczarski, injured three guards at a prison in northern France with
scissors and a razor blade.
Tensions had already been running high after two inmates at the Fresnes prison near Paris were caught discussing a planned attack just days before
they were due to be released.
"We don't have the resources in terms of people or equipment to handle this. We don't have the training to handle radicalised detainees," said Guillaume Pottier of the UFAP-UNSA union.
"The thing that keeps coming up is, 'We're putting our lives on the line for 1,500 euros a month'," said Martial Delabroye, a Force Ouvriere union official at the Reau prison near Paris.
New approach to prison radicals
France's prisons house about 500 people charged with terrorism activities, and about 1,200 inmates are identified as having extremist views.
The government, whose policy has long been to regroup inmates linked to jihadist activities, revealed in November that it had been experimenting with a "de-radicalisation" programme for a handful of prisoners.
For the past year 14 inmates -- eight men and six women -- have been in open custody overseen by a team of educators, psychologists and religious
The RIVE programme's goal is to "disassociate them from extremist violence," said its director, Samantha Enderlin.
But for Benbassa, who met the inmates in December, "these aren't the type of people who attack prison guards".
"English classes, yoga, geopolitical studies, interviews -- all that is very nice, but the results aren't extraordinary," she said.
"The programme isn't for all cases," she told AFP. "We have to start with trying to isolate radicalised inmates, try to find programmes that are viable,
recruit people capable of ensuring real change."
Many French prisons are seriously overcrowded, and the government's other de-radicalisation efforts have not always been successful.
A programme at the Osny prison near Paris had to be shut down recently, Benbassa said, after an inmate attacked a guard using a makeshift blade.
President Emmanuel Macron has promised to present an overhaul of French prisons by the end of February, following years of warnings by guards that their security is at risk.