The RER contains the western world’s busiest train line with over a million passengers a day. It’s become a victim of its own success. In fact moving block signalling was invented to boost capacity on the RER.

The government is currently investing $25B in building more relief capacity, but who knows how much investment you’d need to handle the unlimited travel demand caused by a free fare.

The RER brings riders from the suburbs into the city, but doesn't add to the infrastructure for transporting them once they're in Paris.

There are RER stations within Paris: everything within zone 1 is in the city of Paris:

https://parismap360.com/carte/image/en/paris-rer-map.jpg

But even if cutting prices is within Paris only it will probably affect suburb-Paris traffic, because it changes the cost of a trip to Paris, possibly now cheaper than driving. The article is light on details, but it looks like these measures are taken by the city of Paris with the aim to reduce the traffic within the city.