France's president was heading on Friday to the Alps to be at the side of families traumatised by the savage stabbings of four very young children and two adults, as investigators worked to unravel the motives of a Syrian man taken into custody.

President Emmanuel Macron and his wife Brigitte were travelling together to comfort victims wounded in Thursday's attack, meet their families and people who came to their aid in Annecy, a lakeside town ringed by mountains, the president's office said.

The four critically injured child victims — aged between 22 months and 3 years old — were rushed to hospitals in the French city of Grenoble and Geneva in neighbouring Switzerland.

It wasn't immediately clear if those cities would also be part of the presidential couple's travel itinerary.

Two children remained in critical condition on Friday morning, government spokesman Olivier Veran said. Two of the four children are French and the other two were tourists — one British, the other Dutch.

The suspect, a 31-year-old Syrian with refugee status in Sweden, is in custody. Psychiatrists were evaluating him, Veran said.

The helplessness of the young victims and the savagery of the attack sickened France, and drew international condemnation.

French authorities said the suspect had recently been refused asylum in France, because Sweden had already granted him permanent residency and refugee status a decade ago.

Lead prosecutor Line Bonnet-Mathis said the man's motives were unknown but did not appear to be terrorism-related. He was armed with a folding knife, she said.

Two adults also suffered knife wounds — life-threatening for one them, she said. One of the adults was hurt both by the attacker's knife and later by a shot fired by police as they were making the arrest.