they're wrong.
macs and windows PCs are both compatible with the internation standard of wireless internet, called wifi. For this you need a wireless router, which takes your internet signal from your phone line as usual, and transmits it wirelessly so your laptop can pick it up (it's just a radio signal). Apple produce their own wireless router, and call it the Airport Express. Or, you can buy any other wireless router you like that anyone else makes, and as long as it's wifi compatible (they all are), it'll work fine with your mac. I checked out your "livebox" thingy on the orange website (orange now own wannadoo), and it tells me that it's a wireless router. so it will work with your mac, and you do not need an Airport device.
your problem is how to activate the livebox's wifi signal. this I cannot help you with beacuse I've never seen or used one in my life. But I would be almost certain it should have come with instructions. Maybe someone else on here knows?