The only places where Spanish influenced American accents would probably be in the Southwest and southern California, if I were guessing.
French influence would be mainly just in Louisiana, I’d also guess.
I really don’t think Native American accents have had much influence on American accents, except for New Mexico, Arizona, and maybe Colorado. Could be wrong, just guessing.
Speaking of accents drifting over time, I really don’t think it’s entirely random.
I once heard someone say that Northern and Southern Australians speak differently, and have a similar kind of disparity (in terms of vowels, particularly) that people from the Southern and Northern US do.
I’ve noticed, by listening, that languages from colder regions (Scandinavia, Russia, etc.) tend to have much stronger, harsher consonants, and shorter, less “sung” vowels.
OTOH, languages from warmer areas like Italy, Africa, etc. tend to “sing” their vowels, and to have much less harsh consonants.
I’ve often idly wondered if this is a result of extra muscle tension that results from being in cold weather, and breathing cold air. When I’ve been really cold, I’ve found that everything in the chest/throat/jaw area constricts more, and it’s hard to really open up and relax as I speak.
Over centuries, I wonder if this could actually be partially responsible for accents drifting.
I am afraid this is a observation without any fact in it. Arabic is a language whose speakers are of warm climates and it is no way a language anyone says does not have harsh consonents. Nor is it true of many West African languages, this idea of singing consonents.
How dost I love thee? Yarrr, let me count the ways.
But in a southern accent.
Riddle. Solved.
World, meet Shakespeare.
Studied under Professor Henry Higgins (AKA 'Enry 'Iggins), did you? 
And it’s worth noting that for this example to support your theory, the relationship would have to be reversed (northern Australia being warmer than southern, on the whole).
However in a recent thread on the subject, a number of people claimed that there are almost no regional differences of accent in Australia, which is in itself a remarkable fact given the size of the country. This is counter to what you heard about a distinction between northern and southern accents.
I once heard someone say that masturbation makes you go insane. He was about as right on that as the “someone” you heard. Why on earth would you post guesses and rumored nonsense in a forum devoted to factual answers to questions?
Well ACTUALLY, the Australian DID say it was reversed. He didn’t give any reason for it, but I think he might have believed that there was something about warmer climates that made a predictable shift in vowels.
And bear in mind, until recently, Australia was MUCH more homogenous in terms of the origins of its citizens than the US. The Southern US was settled mostly by Scots-Irish and some British, the Upper Midwest by Germans and Scandinavians, New York City by Dutch, Jews, and Italians, etc., and the list goes on. Pretty much all white Australians’ ancestors are from England, and mostly Southern England, IIRC. It’s apples and oranges.
If you work in call centers for several years you have to find ways to entertain yourself. Guessing locations by accent is one way I do so. I also have a good ear for accents in general, I’ve always had a natural (probably genetic, since my daughter has it too, and her mother DOESN’T) ability re: impressions/accents/voices. It’s nothing amazing, but I’m definitely better than the average person at it.
Why? Because I think it has some real basis in fact, and I’d be willing to bet someone with a PhD in linguistics has come across this idea before, and may even have read an actual published paper on it.
Well I haven’t gone totally insane yet, but my eyesight has gotten to point where I must wear glasses. 
Maybe you mis-typed, but I didn’t say singing consonants, I said vowels.
You’re right, Arabic has some VERY harsh consonants. I attribute that to the fact that it can get pretty cold in the desert at night sometimes, especially farther north in the desert.
Every sub-Saharan African language I’ve heard definitely has a open, “singing” quality to the vowels. Italian does too. Italian is the most beautiful of all the European languages when sung operatically, anyone with a background in opera will tell you that. Composers from other countries would often write librettos in Italian, because the language just sounds so much better than German/French/Russian/English/etc. when sung operatically, with full breath support. Opera singing requires tremendous breath support, because you’re projecting to the back of a large room, and singing over an entire orchestra. Given that, the pinched quality of, say, Russian vowels, doesn’t work well at all.
Here’s a link.
http://ccr.sagepub.com/content/43/2/123.abstract
This study mentions both the quality of the vowels AND consonants, as well an mentioning that the vowels in warm-climate languages tend to be much LOUDER (sonority is the word they use). “Sung” might perhaps be a simpler way to put it, or “sung more operatically”.
When you post a link to an academic paper on the subject, then we can talk. Until then, it’s nonsense. It has all the earmarks of folk knowledge.
I know you already had your reply window open before my post actually showed up, but it is kind of funny that my link comes before your post.
Despite your stereotype, most speakers of Arabic do not live in deserts, nor did they ever. This is as Mace wrote, naïve popular analyses on no base of learning. It is still silly to advance the night hours as explanation.
You then have not great exposure at all to the African languages. Not to the Chleuh, not to the Amhar, to the Songhai, to the Tamahaq, although since singing vowels does not have a definition so it is impossible to have a response. No one who has heard Chleuh would say it even has vowels. And I think it is hard to say Wolof or Peul sings vowels if the comparison is Italian. It is funny because in that region in the colonial days some said the French sounded like birds.
What Mace wanted to say is that in the culture of this place, this forum is for the hard answers and not for the speculation. You are making speculation.
No, I’m posting links. There’s a difference. Can you not click on the link?
You have posted a link to a summary that is not saying what you say, and to read the article to know what the definitions of the terms it requires an abonnement. So I thin k you do not probably. Have that thus you have read the summary and are making a forcing to fit it to your idea.
Uh, actually NOT. The summary specifically says that warm-climate languages make their vowels more audible (which implies LOUDER and LONGER), and that the consonants they use are more vowel-like in nature. It also says they use FEWER consonants and more vowels.
Is this a reading comprehension issue?
The summary specifically says that, while those generalizations are roughly true, they are excessively broad, and don’t hold 100% true in every case. However, it validates the general truth of the trend.
I’d also say there’s a good chance that the amount of time that a particular language has been spoken in a particular climate makes a big difference. Take Russian to equatorial Africa for 10 years, and it’s still going to sound the same. Take it there for 10,000 years, and it’s going to sound pretty different. Not only that, the differences are probably going to be fairly predictable.
This is really starting to get ridiculous. First I’m told I need a study. I provide a study, and now you people act like it doesn’t say what it very clearly does.
I think I’m done with this discussion. The goalposts are getting moved a little too much.