Translation:Some want vegetables, the others want fries.
Yes; in English, we have "some" versus "others." Notice that the French sentence uses the definite article (les uns, les autres). In English, we can put in the article before others: "the others." We can't use the article for the first group, though ('the ones' and 'the some' don't exist). My solution was to say, "Some of them want vegetables, the others want fries." That indicates, as I think the French use of the definite article does, that the entire group under consideration falls into two parts (vegetable-wanters, and fries-wanters, so to speak). It would be slightly but significantly different, in English, if you wrote: "Some want vegetables, some want fries, some want salad" or "Some want vegetables, others want fries (others want salad, etc.)". Les uns ... les autres seems to cry out for a wording like "of them" to be added in English.
The ones isn't used in English in quite this context. We use 'some' to represent that. If you had left the 'the' in, it might have been accepted though, even though it is not how an English speaker would say it. We are here talking about specific people, not people in general over the world, so it's 'the ones - some' and 'the others'. The people who are here.