© Krystyna Richer / Reuters
Weather services say 49.2mm fell in one hour, the French capital's heaviest July deluge on record.
Flooding closed 20 metro stations and three were still shut as commuters made their way to work on Monday morning.
Parts of Switzerland were hit by violent winds and hail storms that also caused flooding at the weekend.
Heavy rain began in Paris at 21:00 (19:00 GMT) on Sunday night and Méteo France said the amount that fell was higher than the previous record of 47.4mm set on 2 July 1995. Rain continued to fall heavily on Monday in Paris.
Some areas of the west and around Paris had seen more than a month's average rainfall between Sunday afternoon and 08:00 on Monday, it said.
While Montsouris park on the southern edge of central Paris recorded 68mm in 24 hours, the western French village of Civray saw 86mm.
Forecaster Patrick Galois said that radar images suggested the central-western regions of Poitou, Berry and the northern Limousin could easily top 100mm in a matter of hours. A dozen storm alerts were in force on Monday as the weather front moved east.
The Paris fire brigade recorded 1,700 emergency calls and responded to 87 incidents, including one in the basement of the culture ministry.
The flooding brought back memories from June 2016, when staff at the Louvre and Orsay museums moved priceless artworks to safety as the river levels on the Seine reached their highest for over 30 years and emergency barriers were raised.
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