Hungary, also a dark horse in qualifying, finished third in their group, behind Romania and Northern Ireland.
Widely viewed as one of the weakest teams in the play-offs, they beat Norway 3-1 on aggregate.
It has been a long wait to see Hungary at a major tournament - their last World Cup appearance came in 1986 and it has been 44 years since their most recent participation in a European Championship.
Their strength mostly comes from the team spirit, forged by former coach Pal Dardai before he was replaced by Bernd Storck in July last year. A lack of genuine star names contributes to a feeling of unity.
Their football has not been exciting and it will take a huge effort from them to pinch points from their rivals.
Fifa ranking: 20
Manager: Bernd Storck
Squad - Goalkeepers: Gabor Kiraly, Denes Dibusz, Peter Gulacsi. Defenders: Attila Fiola, Barnabas Bese, Richard Guzmics, Roland Juhasz, Adam Lang, Tamas Kadar, Mihaly Korhut. Midfielders: Akos Elek, Adam Pinter, Zoltan Gera, Adam Nagy, Laszlo Kleinheisler, Gergo Lovrencsics, Zoltan Stieber. Forwards: Balazs Dzsudzsak, Adam Szalai, Krisztian Nemeth, Nemanja Nikolic, Tamas Priskin, Daniel Bode.
Key player: Balazs Dzsudzsak. Although he has probably passed his peak, he is the undisputed leader and will be a danger from set pieces with his trademark free kicks. The 29-year-old winger is an energetic, skilful wide player who captains the side. But his end product can vary. He knows that he must lead from the front in France to fulfil his early promise. After 76 caps and 18 goals, this could be his moment.