Changes

Public transport in Paris consists of metro, RER (fast trains serving the suburbs with relatively few inner city stops), buses and a few trams. If you're paying for tickets and you'll make a few journeys then the cheapest option is to buy a carnet of 10 single tickets (around 11 euros). You can travel to the end of RER lines for around 15 euros. If you stay several days and will use transports often you can also buy a pass "Mobilis" for one or several days (5,6 € for one day inside Paris), valid on metro, RER and ground transportation, or if you stay for a week or more - the "Carte Orange" for 16.3 € a week (you'll also need a photo for it).

Uniformed inspectors will ask for validated tickets on the train and you maybe subject to the checks mentioned above as well (the RER shares the metro infrastructure). It's possible to travel free but you stand a higher chance of being busted than on the metro. It seems that checks can occur at any time so the best time to travel free is rush hour when controls are impossible. The highest risk of being checked seems to be the on transfer stations from RER to metro