Day one of the Paris Olympics begins with a sense of boundless possibility, as the drizzly dawn breaks and the city awakens after the sodden festivities of the opening ceremony. There is no need for a painfully early shuttle bus through unlovely suburbs to a costly new stadium. Instead, a quick journey on the Paris Métro whisks you to the centre of the city of light and – on paper, or at least Google maps – within a stone’s throw of many of the Olympic venues. Perhaps the whole thing can be done on foot? Paris is so compact! It’s so walkable! Just take a quick stroll along the river or hop on a free city bike and, oh.

Related: Paris 2024 Olympics day one: Dupont going for gold with France in rugby sevens final and more – live

Visitors to Paris 2024 need to learn hard lessons fast. You think you know this city? You don’t. You think Google maps will show you where you need to go? It won’t. You think official-looking folk in Paris 2024 outfits will be able to give you accurate directions? Dans tes rêves, mon ami.

The organisers of Paris 2024 have taken a radically different approach to these Games, vowing that there will be no white elephants, no stadiums so economically unviable that they will be given away to any passing football team in need of a new home. The main athletics events will be held at the Stade de France, the country’s largest stadium, but there will be 15 Olympic and 11 Paralympic venues in existing buildings across the city. Fencing? Where better than the luscious art-nouveau surroundings of the Grand Palais. Archery? How about the backdrop of Les Invalides? And as for beach volleyball – it could only be in the shadow of the Eiffel Tower.

In practice, this means that Paris is the Olympic Village. Only one where the relatively easily managed exterior security barrier is replaced with an endless series of Paris 2024 branded metal barriers, hundreds of bag checks, and – apparently – every single security guard and police officer in the entirety of France.

In this deconstructed version of Paris, roads lead to paths, which lead to barriers, which are closed, and staffed by guards /volunteers/police officers whose directions are as much use as a Frenchman’s promises of fidelity. But this is a country that has suffered multiple terrorist attacks, which has seen its young people murdered in the streets – it will be forgiven for not taking any chances.

The day begins with a beguiling ease, as excitable crowds ignore the rain and pour out of the Métro at Invalides to make their way over the Pont Alexandre III, past the still sodden stands of the opening ceremony along the Seine, towards the fencing at the Grand Palais.

Built for the Universal Exhibition in 1899 and dedicated “by the French Republic to the glory of French art”, it is surely one of the most specular Olympic venues in the history of the modern Games. Inside, its celestial iron and glass ceiling is draped with white tarpaulin to stop natural light from disturbing the athletes, but nothing covers the swirling eddies of its staircases, their sense of eternal movement a fitting backdrop to the thrusts of the foils on the field of play. A small boy, the tricolour painted on both of his cheeks, watches on with rapt attention. “He fences in a local club,” says his father. “So to be here is quite special.”

From the Grand Palais it’s a short 15 minute walk to the Place de la Concorde, home to the Parc Urbain, which is hosting the 3×3 basketball, street and park skateboarding, BMX freestyle and the newest sport at the Games, breaking. However, it actually takes about an hour and a half, via a bad-tempered altercation with a senior security guard, multiple dead ends and several barricaded roads.

The venue has taken over much of the Jardin de Tuileries at the foot of the Louvre, where the newly lit Olympic cauldron flies from sunset until 2am. On the opening day, however, it remains earthbound. Beyond the barrier that separates neck-craning visitors from a closer look, plumes of steam rise into the air as the rain hits its eternal flame. Thwarted, onlookers stick their phones above the barriers, then look down at their tiny screens. One man jumps, futilely, to get a glimpse. “Can’t see a thing,” he says.

In any case, the Parc Urbain itself is empty. The rain, which has morphed from a soft summer caress to a relentless deluge, has made the half-pipes of the street arena slippy and scuppered the men’s street skateboard event, which will now take place on Monday. Onward!

A few stops on the double-tier RER C along the Seine and we arrive at the golden dome of Les Invalides, originally a retirement home for former soldiers, now a collection of museums and – for the duration of this Games – home to the archery, the finish line of the marathon and the starting point for the road cycling individual time trials. Damp but cheerful crowds line the route, below the gilt-winged steeds on the Pont Alexandre III. “Allez, allez!”, they cheer as the women zoom past, eyes ahead, mouths lines of concentration. Among their ranks, Great Britain’s Anna Henderson who won silver on her Olympic debut.

From there, another short zip along the banks of the Seine brings the intrepid Olympics fan to the pièce de résistance of this remarkable Games: the sandy courts of the beach volleyball underneath the Eiffel Tower, built as the centrepiece of the 1889 Paris Exposition to commemorate the 100th anniversary of the French Revolution. The Champ-de-Mars public green space, perhaps the prime lounging venue of the French capital, has been replaced with uncovered temporary stands, filled this opening day with several oilfields worth of plastic ponchos. But a DJ pumps out high energy music, and athletes and crowds both seem impervious to the rain as they cheer the players on.

Paris’s most renowned landmark looks imperiously down, as the party unfolds below. Like the city it represents, it cares little if the spectators are there or not, if moving around its city has been tiring, if medals will be won or lost. When the scaffolding is deconstructed, the barriers removed, the police sent back to their home towns – it will remain. Olympics or no, we will, thankfully, always have Paris.