Put a new battery in the remote then re-synchronise the remote to the car.
The instructions here
http://www.programyourkeys.com/Renault_Laguna_II_Key_Remote_Control_Fob_Transponder_Programming.html
should help, depending on the year of your car. They are for the Laguna, but work on the Megane too.
There are other things which can cause your problem, but start with the cheap and easy stuff.
gaffa
May 2009