Translation:Please give me that red one.
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".
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]
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.