Taoiseach Enda Kenny is holding talks with French president Francois Hollande less than a week on from the Nice terror atrocity.
The fallout from Brexit and security and counter-terrorism measures are expected to dominate discussions at Government Buildings in Dublin.
Eight-four people were killed when Tunisian Mohamed Lahouaiyej Bouhlel drove a truck into crowds enjoying Bastille Day celebrations and fireworks over the Promenade des Anglais in Nice.
Another 15 people remain critically ill in hospitals.
Mr Hollande’s trip to Dublin had been arranged before the terror assault and has since been scaled back, but he has retained a commitment to meet president Michael D Higgins.
He will be back in Paris for talks with British Prime Minister Theresa May this evening.
The discussions in Dublin will be attended by Foreign Affairs Minister Charlie Flanagan and by Dara Murphy, junior minister for European Affairs.
President Hollande, who has already visited Portugal this week, will be accompanied by Harlem Desir, France’s Secretary of State for European Affairs.
On the ramifications of Brexit for Ireland’s so-called soft border with Northern Ireland, Mr Kenny reiterated that it should remain.
“We do not favour a hard border. Obviously we do not want to see a European border from Dundalk to Derry, that would not be acceptable,” the Taoiseach said.
“We’d be vigilant in terms of people moving through who might have tendencies to be involved in terrorist activities.”
Mr Hollande called for greater sharing of information between countries facing the terrorism threat.
“We have to exchange as far as possible information to track a certain number of individuals and avoid any doubt setting in,” the French leader said.
On the Irish border, Mr Hollande said he understood the concerns about ensuring the peace process is not damaged by Brexit.
“I do recognise there is a special situation here for Ireland,” he said.
“It’s a special situation and it has to be found a special place in the negotiations.”
The discussions in Dublin also focused on international and domestic security, the economies and issues relating to energy.
Mr Kenny said Ireland was working on laws which may allow data and information on terror suspects in Ireland to be shared with Britain.
“Obviously where information might be available, which might be tracking terrorist activities or communications, this is an important priority for Ire to assist in preventing terrorist activities,” he said.