The French President was in Dublin for talks with the Irish leadership that focused on "Brexit" and issues of international security.
The two leaders said the activation of Article 50 of the Lisbon Treaty, which triggers the process for an EU member state to leave the block, would allow the start of methodical negotiations, EFE news agency reported.
They also highlighted the importance of maintaining close relations between the EU and London in future.
"Ireland and France are Britain's nearest neighbours, with significant and complex economic, human, cultural and historical links," a statement said, adding that "In consequence, both countries have specific and indeed unique concerns to be addressed in future negotiations".
When asked about the possibility of Britain being granted a concession to access the single market, Kenny said this privilege goes along with the free movement of people.
Hollande is on a one-day visit to the Irish capital to participate in various engagements. His visit is cut short due to last week's terror attack in Nice.
He will also meet Irish President Michael D. Higgins before returning to Paris where he will meet Britain's new Prime Minister, Theresa May, to discuss "Brexit".
This website uses cookies.