So, you recently bought this Megane and now you've fixed the reversing lights. Have they not worked for the whole time you've had the vehicle?
I'm not too good on Megane's but isn't the reversing light switch on the gearbox? And you say the wire had just come off?
I'm wondering if somebody disconnected the wire to disguise something else.
Try disconnecting it again and see if this improves the starting issue. If so, you know where to start looking.