By Crispian Balmer

FLORENCE, Italy (Reuters) - European Commission President Jean-Claude Juncker took a swipe at Britain on Friday, saying he would not give a speech in English because the language was becoming less significant following Brexit.

"Slowly but surely English is losing importance in Europe," Juncker told a conference in Florence before switching into French and drawing applause from his audience of EU officials, local leaders and Italian students.

Juncker, who hails from Luxembourg, speaks several European languages fluently and regularly uses English at international gatherings. He said he also wanted to speak French to be better understood in France ahead of Sunday's final presidential election round.

The conference, on the state of the European Union, comes at a time of tensions between Brussels and London ahead of formal negotiations over Britain's withdrawal from the 28-nation bloc.

Juncker said Britain's decision to leave was "a tragedy".

"We will negotiate fairly with our British friends, but let's not forget that the EU is not abandoning the United Kingdom. It is the other way around. And that will make a difference in the years ahead."

Speaking in English, the European Commission's chief Brexit negotiator, Frenchman Michel Barnier, said a priority in the talks would be to guarantee rights for some 3.2 million EU citizens living in Britain and for some 1.2 million Britons living in EU member states.

He said protecting these rights was "a moral duty".

"Nevertheless we can be certain that Brexit will inevitably entail a number of negative consequences. This is not a question of 'punishment'. These negative consequences simply follow logically from the choice made by the British people."

NO SECRECY

British Prime Minister Theresa May said this year that she had offered to guarantee the rights of EU citizens in Britain immediately but that this idea had been rejected. Barnier denied that others were to blame for the ongoing uncertainty.

"The only cause of uncertainty is Brexit," he said.

He also dismissed suggestions in London that the talks should be largely secret. "I will do everything in my power to ensure that information on the negotiations is made public so that an informed debate can take place," he said.

In a sign of growing friction and frustration, May accused EU politicians and officials on Wednesday of seeking to sway the outcome of a June 8 national election in Britain by issuing threats over Brexit.

A German newspaper at the weekend gave a damning account of a dinner last week between May and Juncker, reporting that he had told May that Brexit could not be a success.

The president of the European parliament, Antonio Tajani, told the Florence conference that no one was looking to undermine May, who says she called the snap election to strengthen her hand in the Brexit negotiations.

"No one wants to interfere in the British elections. Rather, we are happy that at the start of this process there will be a stable government with a mandate to resolve this problem," Tajani said.

Juncker acknowledged that the European Union had its "weaknesses" and was partly to blame for the British decision to abandon ship. But he said the bloc's successes, including helping maintain peace between nations, were often overlooked.

"We are criticized, torn to pieces, but elsewhere in the world we are admired," he said. "We have overcome decades, centuries of bloodshed."

(Editing by Robin Pomeroy; Editing by Tom Heneghan)