Slovakia's SITA news agency quoted Barnier, who is on an official visit to Slovakia, as saying the French government took seriously recent opinion polls suggesting a majority of people were currently intending to vote against the constitution, although he believes opinions will change by polling day.
"I believe that, in the end, the French people will opt for common sense and will prove that the idea of Europe, based on mutual, improved protection, on mutual development, will remain today as well in the future the right idea," Barnier said.
Barnier added it was not clear what the European Union would do if a member country rejectrf the constitution.
At least six recent polls have indicated the no vote is ahead in France where a May 29 referendum is scheduled.
All 25 European Union countries must ratify the constitution for it to be approved. Some countries are holding referenda, while others will vote on it in national parliaments.
Notable deaths of 2014 [PHOTOS]