Arkansas is a French variant of the Siouxian word Quapaw (also a tribe located in the area around the area where Kansas, Missouri, Oklahoma, and Arkansas almost meet, and, additionally, a town in northeastern Oklahoma, between Miami and Baxter Springs, Kansas). Quapaw means, literally, "downstream people." see http://www.straightdope.com/mailbag/markansa.html

It seems that Arkansas retained the French pronunciation, while Kansas went with an English spin. The Arkansas River which runs from Colorado, though Kansas, Oklahoma and Arkansas, is pronouced like the state of Arkansas in Colorado, Oklahoma, and Arkansas, but while in Kansas, it is pronounced "Are Kansas". see http://boards.straightdope.com/sdmb/showthread.php?threadid=72271