"A Frenchman must be always talking, whether he knows anything of the matter or not; an Englishman is content to say nothing when he has nothing to say."

That quote by 18th-century author and poet Samuel Johnson is a good marker to define the love-hate relationship between France and Britain over the centuries.

Georges Clemenceau, who had two stints as French prime minister during the Third Republic, also did his best to ensure there was little love lost when he remarked that "English is just badly pronounced French."

Current French President Emmanuel Macron would probably beg to differ with Johnson's assessment, especially given the mostly positive feedback he's received for his EU "reset" plans, while UK Prime Minister Theresa May seems to have a lot to say without actually saying anything.

And while Macron's gesture to loan the famed Bayeux Tapestry to Britain will be welcomed in the art scene, it might also raise a few hackles, depicting, as it does, the Battle of Hastings when William the Conqueror from France defeated English forces in southern England.

Traditionally, France and Britain have worked closely on defense and security issues within NATO and the EU and globally as Europe's only members of the UN Security Council.

Will Britain's exit from the EU curtail that cooperation? And what impact will Brexit have on their border and economic ties?

Defense/Security 

In 2010, the two countries signed a landmark Defense and Security Cooperation Treaty, known as the Lancaster House Treaties. Under this deal, cooperation increased between British and French Armed Forces in terms of sharing and pooling materials and equipment. It has also provided mutual access to each other's defense markets and allowed for the exchange and development of industrial and technological projects.

According to Nicholas Startin, Head of Department and Senior Lecturer in French and European Politics at the University of Bath, this is one area that could remain unaffected by Brexit. "I think both countries' leaders are sufficiently pragmatic that they will want these arrangements and the relatively close ties that they have on security-based issues to continue."

Still, in the wake of Brexit and with waning influence, the British will have the painful task of developing new alliances if they want to achieve their foreign policy objectives. Alongside all these bilateral agreements, the crucial one will be negotiating a new "special relationship" on defense and security with the EU.

Border issues

In 2003, the two countries signed an agreement known as the Le Touquet accord which effectively saw Britain's border extend into France. Since then British border guards have been stationed in northern France, while French officials carry out immigration checks in the Port of Dover, a win-win situation.

"Within the context of the EU this arrangement seemed to work quite well from a British perspective. What that has done irrespective of the Brexit situation is that it has put huge pressure on the Calais area and the Pas de Calais region as a whole, as it has led to a blockage of refugees trying to get to the UK and an unfolding humanitarian crisis," Startin told DW.

But now France is putting pressure on the UK to take in more refugees and to pay more for border security if the current arrangement is to be maintained. From the French perspective, says Startin, that's reasonable. "I think it's understandable that the French president questions how the treaty operates in a post-Brexit environment, because it seems to me that it is putting an enormous burden on France as many refugees continue to attempt to reach the UK."

And it seems that the cards are in Macron's hands on this particular issue. "The ultimate dilemma for the UK government is that Macron could say 'we want to park this treaty in the long grass' and imply that Dover becomes the border rather than Calais and that's something, that given the political context, the UK the government will be very keen to avoid even as a veiled threat."

Economy/Brexit

In the event of a "hard" Brexit in which the UK leaves the Single Market, the most immediate impact would be on customs-free, cross-Channel trade.

"Obviously the prospect of imposing customs controls and possibly tariffs between the UK and France, in particular those between Calais and Dover where a huge amount of goods travel back and forth completely unhindered by border controls at the moment, is a big issue," Jonathan Portes, Professor of Economics and Public Policy at King's College London and a Senior Fellow of the Economic and Social Research Council's "UK in a Changing Europe" initiative, told DW.

Read more: Brexit: What's the 'no deal' fallout for the UK and EU?

Notwithstanding the nature of Brexit, Portes thinks that "the French will continue to be one of the largest single trading partners [of the UK] under almost any conceivable circumstances."

Nick Startin is not so sure. "It's going to be difficult for the UK to negotiate a meaningful trading relationship with individual EU 27 states in the context of a hard Brexit. At the same time it's also not clear that bilateral economic relationships are going to be that easy to set up in the short term with other countries outside the EU in the shadow of the uncertainties caused by Brexit."

Macron has said repeatedly that he's not aiming to "punish" the UK, but by the same token he remains a passionate European who will seek the best deal for both France and the EU, for which he needs help from Europe's leading economy, Germany.

Avid conspiracy theorists may see this as proof that the Paris and Berlin are ganging up on the UK, which in turn is trying to prevent that axis.

"It is probably true to say that the French are somewhat more hard-line than other countries or more purist in terms of Brexit," says Portes. "On the other hand, so far at least, there is absolutely no evidence to suggest that Germany under Angela Merkel is any less purist on the question of the integrity of the Single Market. The idea that the UK either can somehow try to split France from Germany or isolate France is not a strategy which has any serious prospect of success, and one would hope that our government is not foolish enough to attempt it."