Minister for Foreign Affairs Dermot Ahern
He claimed a number of extreme right-wing groups in France had used the issue of Turkey's application for membership to strengthen to No campaign.
Mr Ahern warned that if the French vote result started a rolling 'no' with Dutch voters on Wednesday it would cause "a severe difficulty".
Former Labour leader Ruairi Quinn expressed his party's "sorrow" at the yesterday's result.
But Mr Quinn, who is also chairman of the European Movement, claimed the treaty itself was not critically attacked.
He said: "The rejection of the treaty by the French public appears to have more to do with their dissatisfaction with the present right-wing government than a disillusionment with the European project which France has done so much to shape".
Last night the Government said the European Constitution was "strongly" in Ireland's interest.
It said it very much regretted the outcome of the French referendum but "fully respected" the voters right to "make their own decision".
It said the Government was continuing to prepare for ratification of the constitution by November 2006.
"We have recently published the Referendum Bill and look forward to the start of debate in the Oireachtas.
"The Referendum Commission will shortly be established and the Government will soon be publishing a full White Paper to help inform the public.
"The Government remains firmly of the view that the European Constitution is strongly in Ireland's interest and in that of the European Union as a whole."