Well, as this thread is turning into a French bashing operation, I want to add my 2 cents, here. I am a French-Padi-certified-living-in-the-States diver.
First thing first: We sent you Lafayette against the Brits, you sent us Ike against the Nazis. I probably wouldn't be typing these words otherwise and am forever grateful. The Americans feel that the French are arrogant. The French feel that the Americans are arrogant. The Americans love traveling to France. The French love traveling to the States. It's a never ending love/hate relationship.
Second: CMAS is not French. It's an association of national agencies comprising France, Germany, Belgium, Italy, Spain, etc. and yes, even the USA. They subscribe to the same diving principles. 90 local agencies representing 90 countries are part of it.
Anyone can try and have fun on the board trying to stage a war between the US and France. I don't believe that it is the board's purpose. However, what we have here are 2 different opinions, 2 different philosophies about diving. And under the First Amendment, they're both equally protected.
CMAS does not make any major difference between rec diving and professional diving. It's all a matter of levels and furthering your education. CMAS was formed in 1958.
PADI is all about rec diving with no decompression and a maximum depth of 40 meters / 130 feet. The Padi no-deco table was created in 1988.
Everybody pretty much agrees that deco diving is statically more dangerous than no deco diving. By the same token, I don't know if the "limit" should be 40 meters, 45 or 35 meters, but everybody will agree that the deeper you go, the more hazardous it gets.
PADI's philosophy is that there's plenty to do and to see within the 40m/130ft limit and that the no deco limits allows for enough time under water. CMAS' members will say: "I want to know what's beyond 40 meters and I can spend more time at that depth if I'm trained for it and manage my air properly". Again, some people like to play tennis, others like to go rock climbing. One activity is clearly more dangerous than the others. Does that make one any better than the other?
One big difference between PADI and CMAS is that PADI is a for-profit publishing company where CMAS and the FFESSM are not-for profit, like most non-professional sport associations in Europe. I have friends who have left PADI because they wanted more. I have other friends who have left CMAS and went for PADI because they wanted a less aggressive/more relax agency.
Bottom line: we all dive together. We just don't train together. At the end of the day, I think, no matter what the agency, it all comes down to your training and experience and where you feel the most comfortable.