New French President Nicolas Sarkozy has moved to prevent friction over Turkey's EU membership bid in the run-up to next month's EU summit.
Mr Sarkozy wants the EU to offer Turkey a "privileged partnership"
A French presidential official quoted by Reuters said Mr Sarkozy - who opposes the bid - would not block further EU-Turkey accession talks.
Mr Sarkozy's top diplomatic adviser held talks in Turkey at the weekend.
Turkey's EU entry talks have been dogged by disputes, including links with the divided island of Cyprus.
The EU suspended negotiations with Turkey in several, but not all, areas because of Ankara's refusal to open its ports to Cyprus, an EU member state.
The French news website Le Figaro says Mr Sarkozy will not veto the scheduled start of EU talks with Turkey on three more "chapters" in the accession negotiations. They are set to open on 26 June.
Mr Sarkozy does not want a dispute over Turkey to undermine his drive to revise the EU constitution, Le Figaro reports.
His aide Jean-David Levitte visited Ankara at the weekend to explain France's position.
Mr Sarkozy has said a simplified treaty is the only way forward to replace the stalled EU constitution.
Voters in France and the Netherlands rejected a proposed constitution in referendums two years ago, leading to the current deadlock.
The constitution needs the backing of all 27 nations of the EU.