For two leaders recently embarrassed by chatter about their behaviour behind closed doors, the smiles lighting the faces of Gordon Brown and Nicolas Sarkozy seemed as unlikely as they were fulsome when the pair appeared for their lunchtime press conference yesterday.

Perhaps they had bonded over their shared adversity. Or maybe they had been cheered by the realisation that they had something else in common – a mutual distrust of David Cameron.

The French leader came as close to endorsing Mr Brown's campaign for a fourth Labour term as the age-old art of diplomacy would allow, lavishing praise on the Prime Minister for his work during the financial crisis, while admitting to his own concerns over Mr Cameron's decision to pull the Tories out of the EU's main centre-right grouping.

Mr Cameron's pledge to leave that European People's Party (in order to secure crucial votes from Eurosceptics during his bid to become leader in 2005) is a decision that could lose him some important friends.

It left the Tory leader scrambling to quell any rancour when he met the French President later in the day, assuring him that Britain would be an "active and energetic" participant in the EU if he became the next prime minister. Indeed, the meeting had been their "best ever", a Tory spokesman desperately insisted.

Mr Sarkozy was here to hold Mr Brown's hand in view of the photographers – and Angela Merkel may also visit Downing Street before the election, another European leader lining up to offer tacit support to Mr Brown's election campaign.

The French President deployed landmines in Mr Cameron's path, insisting, unprompted by any questioning, that Britain needed to remain "bang in the middle" of Europe.

He pleaded, "We need you", and insisted, "I don't want to meddle in domestic affairs" before adding, pointedly: "I'm very happy to work with a British Labour Prime Minister."

For the gaggle of journalists packed into the No 10 briefing yesterday, the vagaries of Tory European policy were not the main event. They were all waiting for someone to ask Mr Sarkozy "that" question.

While Mr Brown has had to endure days of headlines alleging that he bullied staff, the Gallic rumour mill has spun that both Mr Sarkozy and his wife, the musician and former supermodel Carla Bruni, have been enjoying extra-marital affairs.

According to the latest unsubstantiated internet tittle-tattle, the president had a fling with Chantal Jouanno, 40, the junior environment minister and former French karate champion.

When the inevitable question was delivered to the stony-faced President, delicately phrased by a brave French journalist, Mr Sarkozy dismissed it as "idiotic".

"You must know very little about what the President of the Republic actually has to do all day long!" he fumed at such fripperies. "I certainly don't have time to deal with these ridiculous rumours, not even half a fraction of a second.

"I don't even know why you use your speaking time to put such an idiotic question."

Mr Brown, not known for his repartee, wouldn't have been the most likely candidate to lighten the mood. Yet filled with a sudden zeal to rescue his new best friend from an unwelcome confrontation, he jumped in. "As far as the British press, I have been able to tell Nicolas that I don't believe everything that I read in the British press," he chuckled.

Amazingly, it worked. Mr Sarkozy stepped back from the brink – just. "I love Britain. Don't make me bite back those words," he warned, half joking.