Having drawn their first two matches, PSG were unable to find a breakthrough at home.
They are now six points behind rivals Marseille, who went top with a 1-0 win away to champions Montpellier.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.