American 3ds, but I’m in France

The 3DS, unlike the Nintendo DS before it, is region-locked. There are 3 regions: North America, Japan and EU/Australia. So if you buy your 3DS in Australia, you'll need to purchase games from either the EU or Australia as well. Nintendo explained their reasoning in the following statement:

“Nintendo 3DS hardware is available in three versions: Japanese, American and European/Australian,” Nintendo told us in a statement.

“Nintendo has developed different versions of Nintendo 3DS hardware to take into account different languages, age rating requirements and parental control functionality as well as to ensure compliance with local laws in each region. Nintendo 3DS also offers network services specifically tailored for each region.”

It went on: “Additionally we want to ensure the best possible gaming experience for our users and there is the possibility that Nintendo 3DS software sold in one region will not function properly when running on Nintendo 3DS hardware sold in another.”

-Source

I'm going to give this an attempt, although I cannot test it.

While searching on the web, most people say the Xbox isn't the factor, but rather the game is. Some are region-locked, and some are region-free.

It appears Halo: Reach is region-free. Taken from Here (more than half way down the page in the Questions section)

Q. Will Halo: Reach be region-free?

A. According to Domenic, Halo: Reach is “world signed,” meaning you can play any regional copy in any region on any retail Xbox 360.

I could not find a specific answer for Halo 3, but I think you will be able to play Halo: Reach with your friends during this LAN party.