Nancy is not a very big city. If you stay in the city-center you will propably find it more easy to walk than to take a taxi or public transportation.
There is only one tram in Nancy. If you don’t live close to a tram-station, there are lots of buses. The bus and the tram cost 1,30 Eur. if you buy one ticket, or you can buy 10 fares for 9 Eur. If you take the tram you have to buy the ticket in advance from the ticket-machine at every stop. The ticket lasts for 1 hour, but if you know you are going to take the tram/bus a lot during a day, you can buy a day-pass (24 hours) for 3,40 Eur.
Nancy has this excellent offer, like many other European cities have, to rent a “City-cycle”. You can pick it up at around 25 stations all over the city and you can leave it at one of them when you are finished. The price is 1 Eur. for a one day ticket. The first 30 min. are free and you then pay two Euro each 30 min. For a seven day ticket the price is 2 Eur, and the same per. 30. min. as for one day ticket. All you need to rent the cycle is a credit card.
I have not used it here in Nancy yet, but I have used something similar in Sevilla, Valencia and London, and I love it!
You are not allowed to stop a taxi on the street. You need to go to the taxi-station or call to be picked up. There is a minimum fare of around 6 Eur. and then you pay a fixed rate depending on time and place.