Two polls in France suggest the Yes campaign in the EU referendum has taken the lead for the first time in weeks, but others still put the No vote ahead.
The Yes vote has taken the lead for the first time in weeks
President Jacques Chirac is to appear on television later on Tuesday to appeal to the French people directly to vote Yes at the end of the month.
Major political figures on the left and right are now backing the Yes campaign.
Both sides still have everything to play for, with about 25% of the French still undecided, correspondents say.
The latest opinion polls in France are contradictory, with some showing the No vote narrowly in the lead, but others suggest that the Yes campaign is finally gaining ground, says the BBC's Caroline Wyatt in Paris.
A CSA poll for Le Parisien newspaper on Tuesday shows 51% intending to vote for the treaty, while an Ipsos poll for the newspaper Le Figaro and radio Europe 1 on Monday showed 53% of voters in favour of the treaty.
FRENCH EU POLLS
3 May: 51% Yes, 49% No (CSA for Le Parisien)
2 May: 48% Yes, 52% No (BVA for L'Express)
2 May: 53% Yes, 47% No (Ipsos polling group for Le Figaro/Europe 1)
2 May: 49% Yes, 51% No (Louis Harris for Liberation, Yahoo!, i-TELE)
30 Apr: 52% Yes, 48% No (TNS-Sofres/Unilog for Le Monde/RTL/LCI)
The previous 25 polls between 15 March and 29 April showed a majority for the No vote
But a Louis Harris poll for newspaper Liberation on Monday showed 51% of voters still intending to vote against the treaty, while a BVA poll for L'Express magazine, also on Monday, put the No vote at 52%.
Twenty-five consecutive polls have pointed to a No vote, putting the opposition at between 51% and 62%.
Mr Chirac is to appear on French TV on Tuesday at 2015 (1815 GMT), in a direct appeal to French voters to approve the EU constitution in the referendum on 29 May.
His last such appearance in April in a staged debate with students failed to impress the voters, but this time he is hoping to persuade them that the EU constitution is good for France and good for Europe, our correspondent says.
Many French trade unions fear the constitution enshrines an "ultra-liberal" Anglo-Saxon style economic model - seen as very different from the French social model - while others believe the treaty seriously threatens France's sovereignty.
The constitution has to be ratified by all EU member states, but many of them are not holding referendums.
The treaty is aimed at streamlining decision-making in the enlarged EU of 25 nations.