Speaking on Thursday at an Action Plan for Jobs press conference, Mr Kenny said no formal request had come from France to the Irish Government requesting aid.
However, Mr Kenny indicated the Government is prepared to send a small number of Defence Forces personnel to Mali or Lebanon to relieve their French counterparts.
“We have said that, within our conditions and our circumstances, we will assist in whatever way we can here, though probably the numbers will be small,” Mr Kenny said.
French president Francois Holland has said his country is at war with IS and the French government this week invoked a mutual defence clause within the European Union’s Lisbon Treaty.
“When I signed the book of condolences at the French embassy the other day, the French ambassador did mention this to me that France is now very stretched,” the Taoiseach said.
“At the meeting of (EU) ministers for defence during the week, the French defence minister invoked the relevant article from the European treaties looking for help.
“It’s a matter for every country as to their own national security and defence position, how they might assist in that regard.
We have been working with the French in Mali, 10 members of the Defence Forces out there doing particular duties. “Now, a formal request has not come in from France yet. It may come through the Minister for Defence, it may be dealing with extra personnel that the French may withdraw from south Lebanon or Mali or whatever.
“The point the French make is that the French president has declared that France is at war in respect of these incidents in Syria. The French defence forces are stretched in quite a number of countries and they may make a request for assistance in that regard.
Obviously, there is a process by which Ireland being a neutral country would offer assistance in particular forms and we would consider that when it comes.”
Mr Kenny also said the national security committee – which includes Garda Commissioner Noirin O’Sullivan and the Defence Forces Chief of Staff, Vice Admiral Mark Mellett – briefed him, Tánaiste Joan Burton and Minister for Justice Frances Fitzgerald this morning.
“The Tánaiste and I and the Minister for Justice and the Minister for Foreign Affairs and the Minister for Defence had a briefing this morning from the national security committee, including the Garda Commissioner and the chief of staff of the Defence Forces,” Mr Kenny said.
“The situation insofar as Ireland has concerned has not changed since the Paris attacks. An incident is possible but not likely.”