No, but a fifteen or twenty minute walk or bike ride can lose out to a free bus. At least some walkers will be enticed onto the bus, which will require more capacity, which will then improve frequency, which will then attract some more walkers, rinse and repeat.

Above a certain frequency buses become extremely unreliable and dwell times start impacting travel time because bus stops only have so much room. With trains you have more room to work with, but once you run out the marginal cost of building new lines runs in the hundreds of millions, if not billions of dollars.

That's exactly what paying for services is designed to avoid.

When services are made free, people have to wait longer, paying with their time instead of with money.

People who don't want to wait and are not given the choice of paying for faster service end up having to buy cars instead, making traffic worse for everyone.

Alright, what if it's a mile or two? When I was a student I used to walk a few miles a day around town because I didn't want to pay for a transit pass. I was young, broke, healthy (and the walking helped me stay that way); I didn't particularly enjoy walking but liked walking more than I liked spending a dollar on a bus fair.

I don't think you can write off the decrease in foot traffic free public transit would cause.

Not sure how the fee works in Paris to this demographic, but elder people will usually rather use the bus probably.