On Friday we'll be treated to the unlikely sight of many of the cabinet’s big hitters setting off to Paris for meetings with their French counterparts.

The prime minister will be crossing the channel with Nick Clegg. Also attending are foreign secretary William Hague, defence secretary Philip Hammond and newly promoted energy secretary Ed Davey.

The highlight of the annual summit will be gauging the mood between Cameron and French president Nicolas Sarkozy, who this week confirmed he's to fight to keep his job in this year's French elections.

We all know about their recent tiffs. Sarkozy told Cameron to “shut up”, called the British PM a “stubborn child [who makes] unreasonable demands”.

Sarkozy delivered “le snub” to Cameron by refusing to shake hands. This happened on the same night as Cameron's infamous "4am veto" on the European fiscal stabilisation treaty, a veto which turned out to be less of a veto than first thought.

Yet for all the froth, France and Britain's relationship could be characterised as the opposite of a duck on water - turbulent on the surface but calm below the waterline.

Despite the fisticuffs there's been the largely successful operations in Libya - achieved without a colossal overspend or extreme casualties.

For Dr Jonathan Eyal, Senior Research fellow at RUSI, the fact France and Britain acted bilaterally is significant.

"Theoretically relations couldn’t be better," he told The Huffington Post UK. "Just think of it, less than a year ago the two countries decided to go into military action in Libya. It wasn’t merely a question of military action but it was an enormous amount of risk-taking at a time when other key European counties like Germany and the Middle East thought it had no chance of success."

But for Eyal the politics in other areas are fairly frosty: "It is a litany of testy exchanges between Britain and France over the last year over the handling of the euro crisis. We have reached the rather curious situation where we had French ministers saying if debt was going to be downgraded in Europe, it had better be downgraded in Britain first – and British ministers saying it should be France.

On Europe Eyal puts it delicately - “there is no meeting of minds”.

Central to the current political gulf is France's unilateral decision to introduce a financial transaction tax. Sarkozy has lead calls for it, threatening to go it alone if no one else supports him. Cameron has already dismissed the idea as “madness”.

No. 10 says that the transaction tax is not on the agenda for this summit, although Downing Street sources accept it might come up in wider discussions on Europe.

Eyal is very sceptical of any movement on the tax: “It's an irrelevant dispute. There is no consensus in Europe about the imposition of a tax. If the French want to shoot themselves in the foot and destroy the chance of creating any financial centre in Paris, then go ahead.”

The main outcome of the summit will be significant moves to further implement the Anglo-French defence treaty, signed in 2010.

But don't expect any further details on how France and Britain will end up sharing an aircraft carrer. "Too early and slightly controversial," predicts Benoit Gomis from the International Security Programme at Chatham House. "We could also expect a joint declaration on Syria, and further announcements on the development of a joint UAVs programme."

(UAVs - unmanned aerial vehicles - are drones, in layman's terms.)

Gomis goes on: "More broadly, the summit will help reassure sceptics that tensions that emerged between Nicolas Sarkozy and David Cameron around the Eurozone crisis won’t be an obstacle in furthering bilateral cooperation in other topics, including defence."

With both Hague and Hammond attending, Britain will be keen to cover other strategic areas.

Julian Brazier MP, member of the Commons defence select committee, highlights procurement as a likely topic. "Britain and France are by far and away the two biggest spenders [in Europe] on military technology," he notes.

The two countries, according to Brazier, will seek closer co-operation militarily as a result of lessons learned from Libya.

"There is room for closer ties on joint military training. France has an exceptional urban warfare facility, while Britain has a special frigate training unit. Britain is already working with Germany on frigate training so the idea of the French and Brits troops training together isn't too farfetched", says Brazier.

So much of the summit will be about papering over cracks, and gusto for Sarkozy at the start of his election campaign proper. But Jonathan Eyal from RUSI says that while the notion of the two countries being on a "collision course" is overblown, most French and British leaders' relationships follow a well-worn pattern: “Every generation of politicians across the Channel, and the current generation has equally discovered, starts by making claims that we are very close to each other – then start to discover how far apart we are.”