Angela Merkel has the shakes. Emmanuel Macron has the collywobbles. And still Europe has no idea who will be in charge as it contemplates a stormy autumn strewn with political booby traps. In Britain, the Brexit deadline of 31 October is the only date that matters. But the EU, fragmented, disputatious and wounded to an extent unusual even by its fractious standards, is taking one day at a time.

Sunday’s special summit is a case in point. It was convened by an exasperated Donald Tusk, the outgoing European council president, after this month’s regular heads-of-government meeting failed to agree on his successor or who will fill other key posts, including European commission president and president of the European central bank. Now they are having another try.

Arguments over who gets what plum job are nothing new. But this time the standoff reflects some more basic, structural problems. Perhaps the biggest is that the Franco-German motor – the axis that has traditionally powered the EU – is stalling. Macron and Merkel are at odds over much more than who can best fill Jean-Claude Juncker’s boots.

Since becoming modern France’s youngest president in 2017, Macron, 41, has lobbied hard for a “European renaissance”, meaning a more integrated EU that acts as a bulwark against reactionary populist-nationalist forces at home and wields strategic influence globally. His open letter to Europe’s citizens in March called for enhanced budgetary, financial and defence cooperation – and an “internal security council” overseeing borders, migration and a common asylum policy.

Merkel, 64, who was a government minister when Macron was still at school, is much more cautious. The German chancellor and her Christian Democrat-led coalition are wary of grand French ambitions, partly because her business supporters worry Germany would end up paying. Merkel, brought up in East Germany under Soviet domination, is wedded to Nato and the transatlantic alliance in a way French leaders rarely are.

Europe’s apparent inability to rescue the 2015 nuclear deal with Iran from Donald Trump’s ravages illustrates the limits of its bid to be a global player. The EU has sought ways to circumvent American oil and trade sanctions, and so prevent the deal’s collapse. But it was castigated last week by Iran for not trying hard enough, and by the US for trying at all.

To defy Washington in this way, albeit unsuccessfully, was unusual for EU leaders. Yet the main reason for their failure was economic, namely the pre-eminence of the dollar as the international currency of choice. Any company or bank that wants to keep on doing business round the world, or in America itself, simply cannot risk US treasury reprisals for breaching sanctions.

“The brute reality, as things stand, is that Europe does not yet have the tools – or the will – to project its power,” wrote Tom McTague in Atlantic magazine. “The euro cannot be a credible alternative to the dollar as a reserve currency until it is radically reformed, and without a credible reserve currency Europe’s financial might cannot match that of the US.” On this analysis, it could be argued Macron’s European vision is the right one.

Europe’s ambitions on the global stage will be further constrained by a clutch of pressing internal problems. EU parliamentary elections last month revealed a continent experiencing extreme political volatility. Rightwing nationalists, such as Alternative für Deutschland, made advances, but so, too, did greens and liberals. The losers, overall, were traditional mainstream centre-left and centre-right parties.

Gilets jaunes protesters on the Champs-Elysees in Paris in March. Photograph: Anadolu Agency/Getty Images

A likely consequence is that the new European parliament will be a less biddable, more unpredictable creature. That will pose critical management challenges for whoever takes up the top EU posts this autumn. And these shifts are mirrored at the national level. Macron, under withering fire from gilets jaunes protesters, struggling with low approval ratings, and harried by a formidable hard-right rival in Marine Le Pen, is fighting to save his presidency. These stresses could push him into more disruptive positions on contentious European issues.

In contrast, Merkel’s reassuring presence has long provided Europe with a sense of continuity and stability. But the “Mutti Merkel” era is coming to a close. Falling support for the CDU, evidenced by state election reverses, has already led her to declare she will not stand for re-election in 2021. Inevitable speculation over her health, after she was twice seen physically shaking in public, will add to uncertainty about Germany’s future course.

The autumn looks troublesome for other reasons, too. The commission is pushing, perhaps unrealistically, for a 2021-27 budget deal – always a divisive issue. Pressure from Green MEPs and climate crisis activists will increase following the failure of this month’s summit to agree a 2050 carbon-neutral emissions target. East European states were blamed, but France and Germany’s inability to collaborate effectively was again cited as a factor.

A dispute between Cyprus, Greece and Turkey over oil and gas exploration rights in eastern Mediterranean waters is potentially turbulent. Meanwhile, rightwing nationalist governments in Hungary and Poland, which goes to the polls in November, remain at odds with the commission over judicial and media freedom and governance issues.

And then, to cap it all, there is the Brexit deadline. EU leaders insist this is Britain’s problem to resolve. But there are tense undercurrents. Once again, France and Germany do not see eye to eye, with the latter more open to another British membership extension. And Macron seems to be itching for a fight with Boris Johnson. Whatever they say now, EU leaders know a no-deal Brexit could ruin everyone’s Christmas.