That is until now, and it's courtesy of Dr. Megan E. Melançon, sociolinguist and Cajun. From the webpage for Cajun English from the PBS series, "Do You Speak American?", Dr. Melançon states:
"Although there are many dialectal oddities in Cajun English, five features strike the listener right away: vowel pronunciation, stress changes, the lack of the /th/ phonemes, non-aspiration of /p/ , /t/, and /k/, and lexical differences. The use of these features has resulted in no southern drawl at all in Cajun English. Cajuns talk extremely fast, their vowels are clipped, and French terms abound in their speech."
Finally, an explanation!
No Southern drawl at all in Cajun English. Since I spent a lot of time growing up around both sets of my Cajun grandparents from Louisiana, I must've developed a Cajun English dialect. I have been told, not by sociolinguists, however, that I do have more of what has been vaguely described as a "Louisiana" accent, especially when I'm tired or tired in that special way when I have had a drink or two.
I'd also add that not only do Cajuns talk extremely fast, but they do so with their hands. The old joke that if you tied a coonass's hands behind her back, she couldn't talk ain't too much of an exaggeration.
I was starting to think that it was because I'm adopted that I didn't have a noticeable accent, but I vastly prefer this explanation. I was adopted at 6 weeks and moved to Texas when I was 3 so I don't think my genetics no matter how Yankee they are (and they are very Yankee indeed) can resist the juggernaut that is a Southeast Texas drawl without a good reason.
No drawl, no foul, right?
