Florin Tene was born on 10 November 1968 in Bucharest, Romania and started to play junior level football at local club, Dinamo under the guidance of coaches Ioan Timar, Iosif Varga and Ilie Balaci, also until his youth period ended in 1987 he was teammate with fellow goalkeepers Bogdan Stelea, Florin Prunea and Răzvan Lucescu.
[1][2][3][5] After one season spent at Autobuzul, Tene returned back to Divizia A football at Flacăra Moreni where he spent two seasons, earning a 4th place in the first one that granted the team the qualification to the 1989–90 UEFA Cup, a occasion which gave him the opportunity to make his debut in European competitions, appearing in both legs of the 4–1 loss on aggregate in front FC Porto in the first round.
[2][3][5][12][13] He played the first half of the 1999–2000 Divizia A season at Rocar București and the second at Argeș Pitești and in the following season he went for a fourth spell at Dinamo where he made his last five Divizia A appearances, having a total of 275 matches and one goal scored in the competition and a total of 15 games in European competitions.
[3][5][14] Florin Tene played 6 friendly games at international level for Romania, making his debut under coach Cornel Dinu on 26 August 1992 in a 2–0 victory against Mexico.
[15][16] He was selected by coach Anghel Iordănescu to be part of Romania's squad at the Euro 1996 final tournament, however he was not used in any games, the same year he played his last international match on 14 August in a 2–0 victory against Israel.