It's interesting to read Shelby Foote's own take on his biases in the bibliographical notes at the end of volumes I and II of his "Narrative". At the end of volume I, he writes:
"One word more perhaps will not be out of place. I am a Mississipian. Though the veterans I knew are all dead ... the rememberance of them is still with me. However, being nearly as far removed from them in time as most of them were removed from combat when they died, I hope I have recovered the respect they had for their opponents until Reconstruction lessened and finally killed it. Biased is the last thing I would be ... If pride in the resistance my forebears made against the odds has leaned me to any degree in their direction, I hope it will be seen to amount to no more, in the end, than the average American's normal sympathy for the underdog in a fight."
That book was published in 1958. By the time of the 2nd volume, published in 1963, current politics had given him new perspective on the issues of the past. He writes:
"I am obligated also to the governers of Arkansas and Alabama for helping to lessen my sectional bias by reproducing, in their actions ..., much that was least admirable in the position my forebears occupied when they stood up to Lincoln."
My view on the books is that Shelby does a very good job of self-analyzing here. He may have slight bias towards the South, but if so, it is small enough that it functions mainly to give the books a personality and so make them more interesting. And any bias towards the South does not extend at all to a bias towards the Confederacy, which is a much different thing.
In any case, I think the 3 books in his "The Civil War - A Narrative" are the best choice for someone who wants both a readable and yet detailed nuts and bolts analysis of the military actions of the Civil War. For someone who isn't quite as interested in getting into the details but wants to know the main story of the politics and battles of the time, I recommend another fantastic trilogy written about the same time, Bruce Catton's "The Centennial History of the Civil War". It's shorter and less detailed so an easier read, and Catton has the remarkable ability to summarize a man in one paragraph in such a way that you really feel you've seen his essence (or to do the same for a situation). It may be the best choice for newbie Civil War trilogy readers.