One issue with public transportation in the US (not so much in the EU) is that everyone assumes that the primary incentive to get people to use it must be cost. As a result, it's usually run on an absurdly low budget, given revenues are only a fraction of costs, and inevitably it ends up not being terribly useful. Which means few people ride it, at any cost.
If you want public transportation to be popular, you need to make it useful. Make it useful enough, and people will use it, even if the prices are similar to, or even higher than, other forms of transportation.
One Parisian above claims that it takes an hour and a half to cross the city to get from one suburb to another, while it takes 20 minutes by car. That, to me, is a sign that there aren't enough buses filling in the gaps. Here in Martin County, Florida the "bus system" appears to be designed to turn tax money into jobs, rather than provide a useful service, with buses spaced an hour apart, taking an inordinate length of time to cross the county, only offered during daylight hours, and providing no effective county to county service. If they ran every ten minutes, with express buses linking to nearby county systems, I'd probably use it, because I hate driving.
On a wider scale (yes, I know this isn't directly comparable, it's to demonstrate the point about usefulness vs price), Amtrak's Acela Express charges passengers orders of magnitude more per mile than, say, the Silver Meteor. It also carries 10-20x as many passengers. Why? Because it's useful. It links major population centers with an hourly service, rather than linking minor towns and cities with a once-a-day service. So people are willing to pay big money to travel on it. Which is why it makes double what it costs, as opposed to the Meteor which makes half of what it costs.
Build a useful service and they will come. You don't need to make it free. In fact, making it free is probably the worst possible thing you can do.