With Paris closed this vacation season for the Olympics, what could be more fun for a train-lover like me than riding Europe’s reliable high-speed trains across the rest of the continent?

Instead of enjoying spontaneous, easy travel, though, I’m getting an education.

It turns out, one reason high-speed rail “works” in Europe is that its customers will put up with inconvenience and uncertainty that Americans would never tolerate.

Germany’s Deutsche Bahn ICE — intercity express — trains seemed like a great place to start: The country has several cities a few hours away from each other, and a short ride from other European capitals as well.

And the Germans must apply their world-famous precision to DB, the largest global railway, no?

The German system, more than three decades old, rivals France’s high-speed lines for global status among railfans.

The first ICE trip I take — a two-hour jaunt from Brussels to Cologne — goes well enough, although not without an ominous sign: It’s 10 minutes late departing and a few minutes late arriving, with no explanation.

It’s most unlike the Japanese train company that, a few years ago, apologized for departing a few seconds early.

But what should have been a four-hour journey from Cologne to Hamburg is a katastrophe.

We arrive at the station and check the departure board; our train is nowhere to be found.

It finally pops up, listed as about to leave five minutes late, and then 10 minutes late, and then 15 minutes late.

Good thing I splurged the extra $60 or so for the first-class carriage, to relax in the DB Lounge for a bit.

(That, and not sitting on top of strangers, is the only benefit you get in first class.)

But no — the lounge is being “fixed,” replaced by a temporary lounge in a separate building that’s a 10-minute walk from the station.

Unlike New York’s Penn Station, DB offers no waiting-room seating for passengers who wisely haven’t paid for the closed lounge, so you just stand around in the heat and noise.

Finally, we get going.

But the on-board screen — with no acknowledgement by train staff — informs us that our arrival will be 20 minutes late.

Then 30.

Then 40.

Then an hour and five minutes.

Then two hours.

Then close to 2½ hours.

A four-hour trip has turned into a nearly seven-hour odyssey.

The only thing we get for this, the on-board café manager informs us, is free water.

Not the chilled bubbly water that costs $4, but a warm box of water.

Worse, the train silently takes on a mind of its own.

It skips an important stop, causing people to miss a Berlin connection.

It adds suburban stops, making us later.

It terminates short of its scheduled final stop, so people heading there must find alternative transit.

The strangest part is that nobody on board questions any of this.

If Amtrak’s four-hour Acela train from New York to Boston were to run nearly three hours late — and, in decades of regular Acela trips, I’ve never had such an experience — passengers would demand an explanation.

Why is the train delayed?

Broken track, operator shortage, weather, sick passenger . . .  give us a reason.

But the weather has been perfect for days, and not a single reason is proffered.

People accept this tardiness and diversion as normal.

Yet a delayed, rerouted train is better than no train.

Part of the fun of a rail-based vacation is that you don’t have to plan; when you’ve seen enough of one city, book passage to the next one.

Nope: For three days straight, all trains from Hamburg to Denmark’s Copenhagen are booked.

Our various legs of the journey also demonstrate that efficient, cheap rail travel requires packing people into cramped, uncomfortable spaces, to a degree that’s uncommon at home.

Eurostar from London to Brussels crowds its ticketed passengers into a sweltering waiting room with inadequate seats (at least there are seats).

An hour-long commuter-rail trip from Brussels to the medieval Belgian town of Bruges is mostly spent standing in unventilated heat.

Passengers open windows for DIY ventilation, so it’s also deafening.

Things are no better in Italy, the European newspapers report, with vacationers complaining of long delays and crowding.

Long-distance rail has its place in the transportation system, of course, in both Europe and the United States. Acela service has improved East Coast travel, for example.

But high-speed rail is never going to rival the car for flexibility and cost on medium-length trips, or the plane for speed and cost on longer ones. 

If you’re able-bodied and non-elderly, and don’t have children to attend to, relying on rail may be a bemusing adventure.

But it’s easy to see why most Europeans take summer trips by air (54%) and car (28%); only 10% rely on rails.

Unless two seats open up on a train from Hamburg to Copenhagen soonish, I’ll be joining them.

Nicole Gelinas is a contributing editor to the Manhattan Institute’s City Journal.