Navas joined Paris Saint-Germain on a four-year contract on 2 September 2019, becoming the first Costa Rican to play for the men's team. He made his Ligue 1 debut 12 days later, keeping a clean sheet in a 1–0 home win against RC Strasbourg. On 24 July 2020, Navas won his 20th career club trophy after beating Saint-Étienne in the Coupe de France final. On 31 July, he kept a clean sheet and saved a spot kick in the resulting shoot-out as PSG defeated Lyon 6–5 on penalties in the 2020 Coupe de la Ligue Final. That win marked Navas' 15th trophy in Europe, matching Rafael Márquez's record for a CONCACAF player. On 23 August 2020, Navas started his 4th Champions League final losing to Bayern Munich 1–0. Navas finished the European campaign with 5 clean sheets, the second most after Manuel Neuer despite having played 191 minutes less.