French President Francois Hollande, who paid a two-day visit to Nigeria last week, issued a statement condemning "the terrorist attacks with the greatest possible rigour".
The last two weeks have been particularly bloody in Africa's most populous country, with nearly 250 people killed in attacks blamed on Boko Haram before the three weekend attacks.
On Saturday, two blasts in a crowded district of the hotbed city of Maiduguri left at least 35 dead, while another 39 were killed in the nearby village of Mainok by gunmen believed to be Boko Haram fighters.
"We are still counting. So far we have counted 35 bodies. Our men are still working with rescue workers at the scene," Borno state police commissioner Lawal Tanko said of the explosions in the Gomari area of the city.
Witnesses said the final death toll could rise and as many as 50 people may have been killed and dozens of homes razed in the blasts.
Hassan Ali, a leader of a vigilante group in Gomari, said many people remained buried under rubble.
He said many food vendors and children hawking in front of a cinema hall in the area were killed while more than 20 houses and shops were destroyed.
In a separate attack on Saturday, dozens of gunmen dressed in military uniform stormed Mainok, 50 kilometres from Maiduguri, firing rocket-propelled grenades and Kalashnikovs and killing 39 people, a resident said.
"They came in around 7:00 pm and opened fire indiscriminately with RPGs, explosives and AK-47 rifles," resident Yahaya Umar told AFP.
"They killed 39 people who were buried this morning and destroyed the whole town," he said.
Military and police authorities were not available for comment on the incident, the latest blamed on the Boko Haram Islamist group in the village.
The insurgents have repeatedly attacked Mainok in the past two years. In July, a separate raid killed 25 people.
Boko Haram which in local Hausa means "Western education is evil", claims to be fighting to create a strict Islamic state in the mainly Muslim north.
The sect has since 2009 carried out attacks across the north and centre of the country, but the violence has in recent months been concentrated in the northeast, the region where Boko Haram was founded more than a decade ago.
