Prince Abdullah:
they are All Regions and so should play on your American player.
While this is partly true, you have to make sure which version you are getting, as several different options are available: the BFI ones are multi-region, I believe; the ones which appeared in Australia are Region 4 I think; and I'm not sure about the French ones (I have them somewhere, just not to hand to check) but they are most likely Region 2.
Then you may need to consider if your U.S. player and TV set can handle PAL- as well as NTSC-standard video; America and Japan for example use NTSC, the UK and Australia use PAL, and France (at least until recently) was SECAM (quite like PAL so it may be able to show you a picture, but possibly only be in black and white).
I am by no means an expert in this field, and know that changes to digital broadcasting have made much of the old NTSC/PAL/SECAM problems obsolete, but forearned is forearmed, and at least you will know that there
could be problems...!
Good hunting!
Update: I knew that something was niggling at the back of my mind, and with a bit of digging I found
a post from Richard, which mentioned that although the Umbrella Entertainment (Australian) DVDs are
marked as Region 4, he found the ones sent to him to be region free.
Sorry for any additional confusion caused!
Update Update: This 2-in-1 DVD which contains both live-action films and can be found on Amazon.com says it is both NTSC and Region 1 - but only has French language features, if that is a problem to you.