Beckham was sent off for a late challenge minutes after coming on in a bad tempered game which PSG won 1-0.
Elsewhere in Ligue 1 St Etienne drew 1-1 with Olympique Lyonnais in the local derby which was also a key battle for third place.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.