Jensen sought a move to a club in the La Liga championship, and signed a one-year contract with newly promoted team Real Murcia in August 2003. Murcia ended last in the 2003–04 La Liga season, and Jensen was reported on his way to a number of German clubs. He was called up to the Danish team for the 2004 European Championship (Euro 2004) in June 2004. He began the Euro 2004 tournament as a part of the Danish starting line-up, and played full-time in the first two matches against Italy and Bulgaria. He was replaced by Christian Poulsen during Denmark's third match, and saw the quarter-final defeat to the Czech Republic from the bench. Back from Euro 2004, Murcia used a clause in Jensen's contract to prolong it for another two years. The extension hindered Jensen from leaving the club on a free transfer, and he was sold to German club Werder Bremen for €1 million in July 2004.