They have eclipsed Paris Saint-Germain with some great attacking football during the past eight months.
But Saturday’s defeat by PSG in the final of the Coupe de la Ligue (the French League Cup) could now derail their whole season.
Coming into this showdown it seemed that Monaco might have a psychological edge over their rivals.
PSG’s collapse at the end of their sensational contest with Barcelona suggested the side might lack heart as well as leadership.
Monaco, by contrast, kept their nerve in the second leg against Manchester City.
Yet on Saturday night PSG answered the doubters with an emphatic all-round performance that restated their claim to be the best side in France, if not Europe.
It was not just the margin of PSG’s 4-1 victory but its manner. They were a goal up inside five minutes and always seemed to have the edge, with Marco Verratti and the veteran Thiago Motta dominating midfield.
Monaco’s seemingly irresistible attack – 133 goals so far this season – produced a glorious move for their first-half equaliser, but could never put PSG under sustained pressure.
Instead it was the PSG attack that went into overdrive, first with the combined pace and movement of Julian Draxler and Angel Di Maria, then with two great strikes from Edinson Cavani.
Cavani tends to miss a lot as well as score a lot – he should have had four in this match – but he is now in the form of his life.
Overshadowed by Zlatan Ibrahimovic in previous seasons, Cavani now has 40 goals in 40 games, matching the best strike rate of his former team-mate.
This was a game where you could admire at least half a dozen players who are likely transfer targets for Premier League clubs in the summer, Cavani among them.
Verratti is one obvious candidate, as is PSG centre back and captain Thiago Silva, but the club is most unlikely to let either of them leave.
PSG’s reserve centre back Presnel Kimpembe, just 21, also impressed in this game in the absence of their usual first-choice, Marquinhos, who is only 22 himself. Adrien Rabiot, also 22, caught the eye in midfield.
But it is the Monaco youngsters who have mostly stood out this season, notably the 18-year-old striker Kylian Mbappé, who is constantly and inevitably being compared to Thierry Henry, especially after his two goals against Manchester City.
On Saturday he was relatively subdued and it was Thomas Lemar and Tiemoué Bakayoko in midfield who presented PSG with most problems, along with the Portuguese Bernardo Silva. All three are still under 23.
Whether Monaco can hold on to all this young talent is an open question. Their immediate worry is how they will cope with the pressure of competing for both the title and the Champions League.
After Saturday’s defeat Monaco manager Leonardo Jardim talked of their lack of experience.
“For several of our young players it was the first time they’ve played in a final.”
How they react will be critical, starting with another cup tie tonight, against Lille in the Coupe de France.
That is one competition they could probably do without, especially as the semi-final takes place over two legs, and the lack of experience and depth in their squad leaves them exposed.
Against PSG they were missing four players, above all Radamel Falcao, and his fitness will be crucial for the two games against Dortmund.
Those matches are the ones that matter for Monaco’s Russian owners, more than the title challenge.
Other competitions “are a bonus” said Monaco boss Vadim Vasiliev on Saturday night. Understandable, perhaps, from their point of view, but regrettable for those fans with long memories.
Monaco last won the French title 17 years ago. They last won a trophy in 2003. The following year they led the title race by 10 points in January, but then the pressure started to tell.
Chasing the dream of the Champions League, they let the league campaign slip. They made it to the Champions League final, beating Real Madrid and Chelsea on the way, but they ended up with nothing.