Long-distance Eurostar and Thalys trains to northern France, Britain, Belgium, the Netherlands and Germany were running late for about an hour, with the exception of one Eurostar train that was delayed for three hours.
Suburban trains to regions north and east of Paris were most affected as no trains were running for several hours, causing "a traffic breakdown," Céline Sibert of the regional Transilien Paris-Nord authority told a press briefing.
The state SNCF railway company expected traffic to be back to normal on Thursday.
A company spokesman said the disruptions were caused "initially by a small electrical problem that should have affected 150 people for an hour but in the end it became so messy that tens of thousands of people were concerned."
The initial cause of the chaos was a problem with an overhead power line between Paris and the suburban town of Mitry.
But angry commuters caused further disruption after jumping from trains blocked for hours and walking along rail tracks, explained SNCF spokesman Antoine Debièvre.
"After waiting for hours in the dark between two stops, they promised that there would be buses... but then nothing," said one commuter. "They must be joking. How am I supposed to pay for a taxi? I don't have any money."
Often overcrowded commuter trains in the Paris region carry more than three million passengers a day.