Suchopárek played in the Czech Republic's opening game of the UEFA Euro 1996 tournament, a loss to Germany. He picked up a yellow card in the next group match against Italy, which the Czechs won against expectations, by a 2–1 scoreline. Suchopárek scored with a header in the last group match against Russia, which finished 3–3 and meant that the Czech Republic advanced to the quarter-finals of the tournament. Suchopárek was shown the yellow card in the first minute of the quarter final match against Portugal, which the Czechs went on to win 1–0 thanks to a Karel Poborský strike. However, since he had received two yellow cards in the tournament, Suchopárek was one of four Czech players to miss the semi-final clash with France due to suspension. He returned to the team for the final against Germany, although again the Germans prevailed, winning 2–1 thanks to a golden goal in extra time.
Time abroad
Suchopárek was one of players from the Czech squad at UEFA Euro 1996 who left the Czech Republic to play in another country after the tournament, signing for RC Strasbourg in July 1996. During his time playing club football abroad, Suchopárek continued to represent his national team, playing the complete 90 minutes of seven consecutive games in UEFA Euro 2000 qualifying. However, despite the Czech Republic qualifying, Suchopárek missed the UEFA Euro 2000 tournament due to a knee injury. Following three years in France with Strasbourg and a further year in Germany at Tennis Borussia Berlin, Suchopárek returned to the Czech Republic to play for Slavia Prague again in 2000.
Return to the Czech Republic
Suchopárek captained Slavia during his second spell. He had surgery in March 2001 following a tear of meniscus, being the second knee operation he had within a year. In 2001, following Slavia's exit from the 2001–02 UEFA Cup in the first round, Suchopárek was sent to the "B" team of Slavia due to inadequate performances. He later moved to SK Kladno to finish his playing career in the Czech 2. Liga. While playing for Kladno in 2004, Suchopárek dislocated his shoulder attempting a bicycle kick. Suchopárek retired from professional football following the end of the 2004–05 Czech 2. Liga, in which Kladno finished fourth and missed promotion to the Czech First Leagueon the last day of the season.
Non-playing career
During his time at Kladno, Suchopárek started studying for the UEFA Pro Licence, which he completed after two years. Following his playing career, Suchopárek became a coach at SK Kladno, where he remained until 2010, when he moved to FK Dukla Prague to become assistant to Luboš Kozel. He is also a coach for the Czech Republic national under-21 football team. At the end of the 2015–16 season, Suchopárek left Dukla, along with Kozel, following the expiry of their contracts. He was named as the new head coach of the Czech Republic national under-19 football team, replacing Pavel Malura.