The side's appearance in France will be its first at a major tournament since the 1958 World Cup.
Players and coaches left their base at the Vale Resort, Vale of Glamorgan, on Saturday and headed to Cardiff Airport.
After a send-off from pupils from Ysgol Treganna, Cardiff, the team took off for a friendly in Sweden on Sunday.
They will then head to France ahead of the team's first game of the tournament against Slovakia on 11 June.

David Crompton, 52, is to step down in November after four years in the post and 31 years in policing.
His retirement comes after a report by Prof John Drew found the force's response to the abuse was "inadequate".
It was commissioned after the Jay Report found 1,400 girls were abused in Rotherham between 1997 and 2013.
In a brief statement, South Yorkshire Police said: "The chief constable's contract runs until November. He will retire after 31 years in policing."
Prof Drew's report, which was published on Wednesday, said the force "regularly missed" opportunities to tackle the problem of abuse and had "seriously under-resourced" its early work.
The report also said several attempts to alert senior officers to the issue fell on "deaf ears".
The Independent Police Complaints Commission (IPCC) revealed it was looking into 200 allegations about the conduct of police relating to child sexual exploitation in Rotherham.
It also said it had 55 ongoing investigations linked to at least 66 officers in South Yorkshire and had received more than 100 allegations linked to officers who have not yet been identified.
In a statement, the IPCC said: "From the moment the IPCC wrote to South Yorkshire Chief Constable David Crompton to advise him of our expectations for referrals following the publication of the Jay Report in August 2014, the number of allegations and number of officers involved has steadily increased.
"We first announced an investigation in November 2014 and that related to allegations raised in the Jay Report against 10 officers."
Aside from the issue of abuse in Rotherham, Mr Crompton also faced criticism when Sir Cliff Richard's home was searched in connection with an inquiry into alleged child abuse in 2014.
The force co-operated with the BBC to enable live TV coverage of the raid, which an independent report found had "interfered with his [Sir Cliff's} privacy and may well have caused unnecessary distress".
Mr Crompton took over the chief constable role in 2012 from Meredydd Hughes after he retired from the post.

Glamis Hall hosted a lunch club, including a three-course meal and activities, at its Wellingborough home.
The hall was transferred to the control of community group Glamis Hall for All at the end of last year.
Wellingborough Borough Council had planned to close it saying the hall was "no longer fit for purpose".
Graham Campbell, whose father had been going to Glamis Hall for 20 years since he suffered a stroke, called the re-opening "just brilliant".
He said: "The people we have spoken to are so pleased. That is what makes it all worthwhile."
About 180 people use the hall's facilities regularly, but the borough council decided in June that the 40-year-old building was no longer fit for purpose and needed extensive refurbishment.
It was deemed too expensive to run and had been supported using discretionary funding that was no longer available.
The council decided to close Glamis Hall at the end of the year sparking a protests from users, their carers and community groups.
Glamis Hall for All was set up in response and raised a 10,000-signature petition to save the centre.
Freehold of the building was granted to the group after it presented a business plan to run it as a community amenity.
The borough council also confirmed the group would be given a one-off capital grant of up to Â£250,000 to help repair and refurbish the building.
Mr Campbell said the group would need plenty of volunteers and would have to apply for more funding.
He said: "We can work on that. No-one thought we would get that far."
Wales' football team has departed the country as their Euro 2016 preparations reach a climax.
[NEXT_CONCEPT]
The chief constable of South Yorkshire Police has announced his retirement on the day a report criticised his force's handling of child sexual exploitation.
[NEXT_CONCEPT]
A day centre for older people which had been threatened with closure has opened for the first time under the control of the group which saved it.