Francois Hollande has said Salah Abdeslam was directly involved in preparing the deadly attacks in Paris in November.
In a joint press conference with Belgian Prime Minister Charles Michel, Mr Hollande said France will ask for Abdeslam to be extradited.
"Salah Abdeslam was directly involved in preparing the organisation and perpetration of these attacks," he said.
He added that the fight against terrorism would go on, and there were "connections that lead us all the time to Syria".
"Although this arrest is an important stage it is not the final conclusion of this story because there have been arrests already. And there will have to be more because we know that the network was quite widespread, in Belgium, in France, in other countries of Europe as well, Mr Hollande said.
"So until we have arrested all those who took part or contributed, financed, that network, that terrorist network that committed the abominable attacks, the war acts of November 13, our fight will not be over until then."
The most wanted fugitive from November's Paris attacks has been detained by police following a raid in Brussels.
Salah Abdeslam is the prime suspect behind a series of co-ordinated attacks in Paris last November which killed 130 people.
He is now in custody after he was wounded during a shootout with Belgian security forces during a raid on an apartment block in a suburb called Molenbeek.
Confirming Abdeslam's arrest, Belgium's Secretary of State for asylum and migration said "we got him".
ITV News Correspondent Paul Davies reports:
The Belgian prime minister has confirmed Paris attacks suspect Salah Abdeslam was arrested in a raid in Brussels.
Charles Michel said Abdeslam was among three suspects detained during the raid in which police faced armed resistance.
Video footage purportedly shows the moment Paris attacks suspect Salah Abdeslam was arrested by anti-terror police after a raid in Brussels.
The 26-year-old Belgian-born French national had been on the run since the attacks which killed 130 died last November.
Belgian newspaper HLN has reported that a third suspect has been captured in a police terror raid in Brussels.
It follows the earlier arrest of Salah Abdeslam - a prime suspect in the Paris terror attacks last November.
One person is reportedly still holed up in a flat where Paris attacks suspect Salah Abdeslam was wounded and arrested on Friday.
Deputy mayor of the Brussels neighbourhood of Molenbeek, Ahmed El Khannouss, told the Associated Press news agency police are still searching for the individual.
There have been reports of gun fire at the scene and police have cordoned off the area.
This image, tweeted by Belgian TV news broadcaster RTL info, purportedly shows the moment Paris terror attacks suspect Salah Abdeslam was arrested by police in the Molenbeek neighbourhood of Brussels.
Abdeslam, who has been on the run since the 13 November attacks, was reportedly wounded in the leg during the raid.
Paris attacks suspect Salah Abdeslam was shot in the leg as he was detained by police in Brussels, the Associated Press reports, citing the deputy mayor of the Brussels neighbourhood of Molenbeek.
A Belgium minister has confirmed Paris attacks prime suspect Salah Abdeslam has been detained in Brussels following a raid by police.
Confirming Abdeslam's arrest, Theo Francken, Secretary of State for Asylum and Migration tweeted "we got him".
The Federal Prosecutor's office has also confirmed Abdeslam's arrest, public broadcaster RTBF said.
Salah Abdeslam, one of the main suspects in last November's Paris terror attacks has been wounded and detained by police in an operation, according to Belgian media.
One other suspect was shot dead in the operation and another wounded, during the raid in the neighbourhood of Molenbeeck in Brussels, the Derniere Heure paper said on its website.