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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?