The nearest metro station to the Eiffel Tower is Champ de Mars. You can take Metro 6 from Vavin, and get off at Champ de Mars. It takes about 20 minutes by metro.

You can also take a bus to get to the Eiffel Tower. Find Bus 82 which takes you there and only takes 18 minutes.

If its a nice day, get a map and walk from Vavin to the Eiffel tower is not a bad idea either. The distance is about 3.5 km and takes about 45 minutes if you don't get lost.