It was meant to be a moment of collective euphoria, with a potential Euro 2016 win offering a salve to France's wounds after the Paris attacks and months of political blues.

But while the 1-0 defeat to Portugal meant crestfallen France did not wake up on Monday to the party it had hoped for, the nation revelled in a rare show of unity after reaching the final and successfully hosting the tournament.

"So cruel," headlined Le Parisien newspaper, summing up the thoughts of many who glumly walked out of bars and fan zones after the excruciating defeat to a goal from Eder in extra-time while Portugal's talismanic Cristiano Ronaldo watched injured from the sidelines.

"We would so have loved a collective explosion of joy. Too bad," the paper said in an editorial.

Tears aside, France's presence in the final had brought a much-needed air of excitement to a country living under a constant threat of terror attacks and dogged by months of violent anti-government protests.

"With everything that has happened, the attacks, the demonstrations, the economic crisis, we deserved something to make us feel better," said a dejected Lazaro de Santana, 31.

French officials hailed the smooth running of the tournament.

"Today we can say that it is France who won. Maybe not in sports, but our country won in its capacity to organise the event," said Sports Minister Patrick Kanner.

While the victory parade took place not in Paris but in Lisbon, President Francois Hollande hosted the French players for a lunch and consoled them with a speech congratulating them on their achievement on reaching the final.

France could at least lay claim to having the tournament's best player after UEFA gave striker Antoine Griezmann the honour on Monday for his six-goal performance.

The tournament kicked off a month ago with anxiety over the jihadist threat and fears over France's image as strikes caused transport chaos and uncollected rubbish piled up in the streets.

"We were all haunted by fear of a terrorist attack. We were fortunate that nothing serious happened and it is a great relief," said Jacques Lambert, head of the tournament's organising committee.

The final was, however, slightly marred by clashes between police and fans who were refused entrance to the packed fan zone at the foot of the Eiffel Tower, with 40 people arrested.

Police fired tear gas to disperse the angry fans, who set alight rubbish bins, a car and a scooter and lobbed bottles at officers.

A spokesman for the Eiffel Tower operator said the landmark would be closed on Monday after the incidents left the ground littered with debris and broken fencing.

Despite violence at the start of the tournament when Russian hooligans attacked rowdy England supporters in Marseille, the spirit of the game quickly took over and fan zones and bars were packed by the closing stages.

The French shrugged off the gloom of recent months as their team swept to the final, beating world champions Germany in the last four.

Despite bemoaning the "cruel outcome" of the final, Le Figaro newspaper said the French team could still be proud.

"France must dry its tears because it has every reason to be proud. The competition was a popular success even though its organisation was tricky with the risk of attacks," it wrote.

"It will remain a joyous digression for a nation which... is in the doldrums. The magic of football worked."

Before the match, Hollande said the French had needed to find a way to unite again.

When Paris was struck by jihadists in January 2015, with attacks on Charlie Hebdo magazine and a Jewish supermarket which left 17 dead, over one million people marched through the capital in a show of unity.

However after a team of jihadists hit Paris bars, restaurants, a concert hall and the Stade de France on November 13, killing 130 people, a semblance of unity quickly dissolved into political bickering.

"The French people needed to find their way again," Hollande said.

However Hollande, who has recorded some of the lowest popularity ratings for a post-war French president, warned that the euphoria of sporting success was short-lived.

"The Euro sweeps away everything else, it brings people together, but life will resume afterwards," he said.