Jake, I have bought tickets from Airasia.com, Garuda, Batavia Airlines, Lion Air everytime online from France through their website and I can assure you that you don't need an Indonesia credit card to buy the tickets. VISA cards are accepted.
Though there are some hints to follow, especially on Batavia Airlines website (or is it Lion Air?), like clicking on a "foreign origin" option, otherwise it will consider you are indonesian and won't let you access to foreign payments.
I was also very impressed with Garuda customer relationship policy : they call you home to verify whether it's not a fraudulent purchase and whether your ticket was the one you needed. They once found a better flight option for us, canceled and replaced the flight for no charges! It's not for nothing they have been awarded Skytrax award 2010 for best improved airline!
On the other hand you have to dogfight with Lion Air to get a refund on a cancelation : they pretend they can't refund foreign Credit cards if you're not in Indonesia, which is wrong. Their english language knowledge is also very limited, it's a shame knowing they pretend and advertize it as their "international" call centre tel number.
I found out the only way to get the refund properly was asking their Singapore office, which is more customer friendly than Jakarta.