PARIS (Reuters) - Former French president Nicolas Sarkozy said on Tuesday many of the faults Britain finds in the European Union are justified and the bloc will need a new treaty regardless of whether Britons vote next month to leave the EU or not.

Nicolas Sarkozy, head of France's Les Republicains political party and former French President attends a meeting in Marseille, France, April 27, 2016. REUTERS/Jean-Paul Pelissier

“On much of their criticism, the British are right,” Sarkozy told Le Monde in an interview. “The peoples’ estrangement from Europe is a major worry for all countries,” he said, while underlining that he strongly opposed Britain quitting the EU.

“But Brexit or not, we’ll need, in all scenarios, to deeply relaunch the European project, and that will have to be done through a treaty that France must initiate, from the summer of 2017,” Sarkozy said.

He did not, however, support the idea of holding a referendum on Europe in France, as mooted by another conservative candidate in the centre-right’s primaries for next year’s presidential election.

British support for staying in the EU has risen, putting the “In” campaign 15 percentage points ahead of their “Out” rivals, according to a telephone poll for London’s Daily Telegraph newspaper whose results were released on Tuesday.

Britain will hold its EU referendum on June 23.

Sarkozy also proposed setting up a group composed of interior ministers of the 19 members of the EU’s Schengen passport-free travel zone, with a stable presidency that would have authority over the EU border control agency Frontex.

He suggested this would improve political accountability and coordination across the EU in handling a migrant crisis.

He further said Europe could not trust Turkey to honour a deal with the EU to halt migration to the European continent, and that Ankara was evolving towards an authoritarian regime.

Turkey refused on Friday to heed EU demands to curb broad anti-terror laws seen by critics as a tool to stifle dissent, and said the EU must find a “new formula” to salvage the deal on migrants in return for visa-free travel for Turks in the EU.

Sarkozy, who lost power to Socialist Francois Hollande in the 2012 election, is widely expected to take part in the centre-right’s pre-election primaries.

In other comments, Sarkozy took issue with criticism by EU institutions of the conservative governments of Hungary and Poland over perceived anti-democratic practices.

“As far as I know, (Prime Minister Viktor Orban) has always respected elections’ verdict,” he said. “You can’t say there is no democracy in Hungary.”

“As far as Poland is concerned, I saw the Kaczynski brothers in power. They respected European rules, and when they lost, they left. After 50 years under the communist yoke, these countries are functioning democracies.”

The Law and Justice Party of Jaroslaw Kaczynski was returned to power in an election last October after several years in opposition. His twin brother, former president Lech Kaczynski, died in a 2010 plane crash.