Translation:That red one, please.
My guess is that this is a problem of reverse translating. In the Japanese version of the English course, "sono" often appears in place of "the" to help Japanese learners of English know that they need to use "the". I don't think it's a good translation method, though. "Sono" means "that", and there is no equivalent to the English "the", though sometimes sono might work in its place.
[Edit to say "the" and "that" are both accepted by the contributors as translations of その, so if one is rejected, it is always worth an error report.]
This is an example of how, in Japanese, certain parts of the conversation (most often nouns and pronouns) are often left out if they are already understood. の here is really more of a placeholder for something that you know can easily be inferred through context.
For example: if you were shopping for a new umbrella, and the store clerk KNEW you were looking for an umbrella (because it's an umbrella shop, or you told them already), it would be considered redundant to say 「赤いかさ」. They know you want an umbrella. So instead you could say 「赤いの」, which basically translates here to "the red [thing we've been talking about]."
This same principle is why a lot of Japanese sentences don't have a pronoun: it's considered unnecessary if people already know who you're talking about.
When talking about substances, "en" in French means "some". But you cannot use it here because we're talking about a countable item (you would use "a few" instead of "some").
So 赤いの would actually be "le rouge", "la rouge" or "des rouges". (The adjective is used as a noun here because the noun is omitted.)
And その赤いの would be either "celui-là rouge" / "celle-là rouge" (that red one), or "ceux-là rouges" / "celles-là rouges" (those red ones).
Adjective + の(は)
The 'one' that...
な-Adjective + なの(は/も)
い-Adjective + の(は/も)
[の takes the place of a noun that is omitted from the sentence・の turns the proceeding clause/adjective into a noun]
You are right that the Japanese sentence has no verb and, as such, it should be acceptable to translate it without using one. However, in English, when there is no verb, the word "please" cannot be placed at the beginning. It sounds very weird and I am not sure why.
So either you put "please" at the end like this: "That red one, please."
Or you add a verb like this: "Please give me that red one."
(Note: It is possible to consider "please" and ください to be verbs. I am not counting them when I say "no verb".)
Just to add, ください is the polite imperative form of the verb くださる (to give me), which is where the "give me" part comes from: https://en.wiktionary.org/wiki/%E3%81%8F%E3%81%A0%E3%81%95%E3%81%84#Japanese
Not really. This is more used to mean "That red item we were already talking about/item you should be able to infer". "Thing" is more general and implies you are just pointing at an object. THe difference is hard to explain but there definitely is one. Someone else might be able to explain better.
"That one in red" sounds to me like your are pointing to something that is not red, and are asking for the same kind but in red.
"That red one" sounds to me like you are pointing to something red, and you want that specific one.
The Japanese is pointing to a specific red thing.