UPDATE: HRTV's website indicates that it will also have coverage of the Arc but it's not clear as to whether that will only be through video streaming or whether it will be on their channel, as well.
According to a banner on their home page, TVG will have live coverage of the 2012 Prix de l'Arc de Triomphe beginning at 8:30am Eastern / 5:30am Pacific. An 8:30am start time would suggest that the network will also broadcast three of the stakes races leading up to the Arc, including the G1-Prix de l'Opera for fillies and mares.
Typically, US TV coverage leverages off of UK coverage, although there have been instances where the feed was simply the raw pictures from Longchamp (along with the French commentary). Since I don't speak French (at least, not well), we'll hope for an English feed.
The 2012 Prix de l'Arc de Triomphe is the sixth race on Sunday's Longchamp card and is scheduled to go to post at 10:25am Eastern time.
Let's hope there aren't any stewards inquiries on Sunday as we might not find out the winner until sometime next week. (That's a joke for all of those that remember the Dylan Thomas year of endless tape review.)