French police have arrested a man suspected of involvement in the shooting deaths last weekend of three people at Brussels' Jewish Museum.

The 29-year-old was arrested in the southern French city of Marseille on Friday and had a Kalashnikov and another gun with him, a French police source told the Reuters news agency.

The man, named by the source as Mehdi Nemmouche, was from the northern French city of Roubaix.

The AFP news agency quoted French sources as Mehdi Nemmouche, a French citizen, while local media reported that he was suspected of having stayed in Syria with armed groups in 2013.

An Israeli couple and a French woman were killed on May 24 when a man entered the Jewish Museum in Brussels and opened fire with an assault rifle. A Belgian man remains in critical condition in hospital.

The French president Francois Hollande said his country would do all it could do to stop a repeat of the attack.

"We will monitor those jihadists and make sure that when they come back from a fight that is not theirs, and that is definitely not ours ... to make sure that when they come back they cannot do any harm," he said.

"We will fight them, we will fight them and we will fight them."

Police released a 30-second video clip from the museum's security cameras showing a man wearing a dark cap, sunglasses and a blue jacket enter the building, take a rifle out of a bag and shoot into a room before calmly walking out.

One of the Israeli victims, Emmanuel Riva, had previously worked for Nativ, a government agency that played a covert role in Jewish migration from the former Soviet Union, an Israel official said.

Miriam Riva, his wife, had also worked in the past for the prime minister's office, the official said.

Source: Reuters And AFP