There is a car sharing service in France called Blah Blah. Passengers have rated "Blah" so you don't have to share ride with people who speak less or more than you usually.
Car sharing services in France are incredibly popular, everyone uses them. This is partly because the government has a monopoly and keeps the trains expensive, and stops buses from running. In the UK, buses are the way to go, you get very cheap buses if you book in advance.
Buses in the US are cheap, but our government monopoly rail service is even more expensive and even slower— NYC to DC is shorter than Paris to Lyon, but costs for a ticket a week out are higher for the low-speed Northeast Regional than the TGV, and our low-speed high-speed train, the Acela, costs more than twice as much as the TGV.
How do private corporations build rail infrastructure without government? Wouldn't you need to negotiate with tens of thousands of private property owners, such that one holdout would be enough to kill the project?
UK buses may be cheap for long-distance travel, but outside of London they're pretty expensive for short distances, often more expensive than sharing a taxi with even one other person.