There are a lot of interesting aspects of human and feline vocalizations to consider here, and while I'll admit I'm not expert, I'm going to attempt to tackle some of them here.
First of all, from this video about humorous cat noises, you can see that there are many noises cats can make. A lot of them sound completely stupid, but I imagine they'll be a lot less laughter-inducing coming out of larger feline species with longer vocal cords. The main problem you run into is that many human languages are made up of dozens of phonemes, or individual sounds; while cats can produce many of them, they most certainly struggle with others.
Something that I learned while researching this (from this article and others) is that
the meow of an adult cat is almost exclusively used to communicate with humans, and not other cats. It may be a variant of the sounds kittens make to call their mothers; cats use meows for a similar purpose, to call to their owners. With this fact in mind, it is conceivable that cats may be able to produce other noises that they have not yet learned to use. Right now, a simple meow does the trick, but with practice and the desire to convey more complex ideas, cats can probably manage to stretch their abilities to cover more phonemes.
Another consideration you should make is that human languages aren't built for cats; thus, there will be a lot of words that are hard for cats to pronounce. Humans get that with their own languages; for instance, I occasionally amuse myself trying to pronounce French words correctly, but I know I would be nearly unintelligible to a native French speaker. But while issues learning a language can usually be solved with practice or by learning when you're young, there will always be some words cats just can't speak. For these words, and probably most of the language, they'll have to speak more slowly, and really be sure to enunciate as clearly as possible.
If you want to know how a specific human language is going to sound being spoken by a cat, first find a list of that language's phonemes(they're not just the letters, for instance here is a list of English phonemes). These are your building blocks, as every word in the language will be made up of them. Next, try and match each phoneme to a cat noise. If some noises cover multiple phonemes, that's fine; it may make the cat harder to understand, but it'll probably be unavoidable. And finally, test out some words, and see what the cat has to do to speak them. Some sounds are going to be hard to put together; for instance, it may be difficult for a cat to switch from a purr to a meow. Transitions like that are going to slow your cat's speech down, but in other places the words may flow just as easily as for a human.
In the end, it's going to sound strange, kinda funny, and nearly unintelligible. But pets always seem to have a way to get their meanings across; I'm sure sentient ones will be even better at it.