A common problem I have with modern science fiction and fantasy (Halo, Mass Effect, Narnia etc) is that the aliens and animals are somehow able to speak in perfect human speech. How does an alien or animal manage to speak in the the phonemes humans are able to?
Having a different anatomy would definitely change things up a bit. They may not have the same consonants as we do, but they may be able to produce some. With a snout, it's possible to have several palatal-like consonants - basically a forepalatal and a backpalatal.
Many birds use a syrinx to produce vocalizations, rather than a larynx like we do. It's a small organ where the throat splits to each lung. It even allows some species to produce two different notes at once. So having phonemic chord in an avian language is certainly a possibility. As for fricatives, they can be done, and so could stops. Again, it's a matter of their tongue shape and dexterity (which could change drastically on the evolutionary road to sapience). While not human speak, Lyrebirds can produce an extraordinary phoneme of their own, but we can do better.
Parrots can produce very near copies of fricatives, so birdfolk would be able to plausibly manage human languages, albeit with a noticeable accent. It would be unlikely to be their native tongue of course, but they may be able to learn.
Honestly, the closest we are going to get to human speak is with birdfolk, not beast folk.