Chief executive Jonathan Ford said the FAW would be working with organisers and others as safety was "paramount".
An army of fans are expected to make the trip for Wales' games in June.
They face Slovakia in Bordeaux, England in Lens and Russia in Toulouse in their first major tournament since 1958.
Plaid Cymru leader Leanne Wood called for 16 June to be made a national civic day so more fans can witness Wales take on England.
She said because the match will take place during working hours, employers should be encouraged to make provisions to allow employees the afternoon off.
Mr Ford said it was hoped friendly matches would be held in Wales before their Group B matches to give the "boys a great send-off".
The majority of home matches since 2011 have been staged at the home of Cardiff City.
The last time Wales played at the Millennium Stadium was the 2-0 defeat by England in March 2011 in front of a crowd of 69,000.
Mr Ford said: "Of course, there are some complications at home. There are concerts that happen in the summer at those stadia.
"We've got to look at that. We've got to put it all together as quickly as possible."
He said Uefa, which oversees football in Europe, took "security very, very seriously".
"Tragic circumstances here, of course, very much mentioned in the ceremony and in the draw," he said, referring to the Paris attacks in November.
"Our focus now has got to be on to the teams, but we will have many people working with us to ensure the environment is very secure for us," he added.

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Defending champion Selby edged past Ding Junhui to set up a repeat of the 2007 showpiece against Higgins, who comfortably beat Barry Hawkins.
Scotland's Higgins last reached the final in 2011, when he beat Judd Trump.
"You'd favour Mark, because he has been more involved in the massive matches in recent years. I've not," said Higgins.
The final - the 41st to be held at the Crucible Theatre - starts at 14:00 BST on Sunday and will conclude on Monday.
Higgins features for the sixth time, and victory would take him second in the all-time list of ranking title wins on 29 - seven behind compatriot Stephen Hendry.
The 41-year-old, who has won three non-ranking events this season and beat Selby 18-13 a decade ago, added: "Mark will not go below a certain level, so I need to play better.
"I know what I need to do in the last, massive game to end the season.
"I am trying to stay focused and give it my all against the number one player in the world. Winning it would be my biggest achievement, without a doubt."
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Englishman Selby is attempting to become only the fourth player - after Hendry, Steve Davis and Ronnie O'Sullivan - to win consecutive world titles in the modern era.
He overcame a stern test against China's Ding, who he beat to claim his second crown in Sheffield 12 months ago.
The Leicester player has been in supreme form this season, winning four ranking titles and reaching the Shanghai Masters final.
Selby said: "It will be a fantastic occasion. I played in my first final 10 years ago against the same opponent and here we are on the 40th anniversary.
"John is a great player, one of the greats of the game. He has had a fantastic season and is in the final again. It will be another tough match for me.
"If he wins another world title, he will be equal with Ronnie O'Sullivan on five victories so he is trying to created history himself."
Former world champion John Parrott on BBC TV:
If there is one player whose game matches up to Mark Selby, who can match him in the safety and tactical departments, it is the man in the final with him - John Higgins.
The Scot is a consummate match player, we have all been there and played him and know what problems he causes his opponents. Higgins will be up for the fight.
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Security will be taken "very seriously" for Wales football fans in France to watch the team at the Euro 2016 finals, the Football Association of Wales boss has said.
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Four-time winner John Higgins says opponent Mark Selby is the "big favourite" for the World Championship final, which starts on Sunday.