I know a few people have asked about best way to get to Menton to Nice Airport. I did it recently, and so thought I would post it here.
Train: Trains from Menton and Menton Garavan station every 30 minutes. You have to get down at Nice St Augustin station (around 45 minutes train journey), then walk for around 500 metres (this is clearly signposted on the footpath), and then take a Bus (Number 23 I think) to the Airport (another 15 minutes or so). The Bus only goes to Terminal 1, so if your flight is from Terminal 2, you need to take a free shuttle from Terminal 1 to Terminal 2. All in all, it took us around 90 minutes once we reached the station. Cost is 8 Euros (6.50 Euros for the train and 1.50 for the bus)
Bus: We didn't take the bus but apparently there is a direct bus from Menton Bus Station to Nice Airport (Bus Number 110) which takes at least 1 hour (or more depending on the traffic). This bus goes to both Terminals 1 and 2. Cost is 20 Euros. Just search for Nice Airport Express for details.
I would recommend taking the train in most cases, but if you have someone very old, or kids or people with special needs, the bus might be a better option as it needs no change.
Hope this helps