First, let's talk about restrictive vs non-restrictive clause.
Restrictive and non-restrictive, both clauses are noun modifiers, but the main difference is, restrictive clause restricts the meaning of the noun that it modifies, we mention a specific, particular noun by introducing restrictive clause.
Whereas, non-restrictive clause is like optional clause, the information does not affect the noun it modifies.

In general,
restrictive clause
1. is introduced by that
2. clause is NOT separated by comma.

non-restrictive clause
1. is introduced by which
2. clause is separated by comma.

Now, in the statement, we are talking about export of a particular, specific wine (the wine), so that is valid here.

I think which would be a valid case if the sentence is like,
Well-informed people know that Bordeaux is a French region whose most famous export is wine, which bears its name. (note: the is missing before wine)

that: introduces the essential part (required to construe the meaning of sentence)
which: introduces the non-essential part (the sentence makes sense even non-essential part is omitted).

Here that bears its name is required information and can't be omitted by using which.

Hope you got the point.

Best,
Shanta

The above is not really something that the GMAT focuses on though. How are you to know which information is essential and which is none essential? As long as you know that "which" has a comma before it and "that" does not you are fine.

The big difference between that and which is that the word "that" has more uses than "which."

The use you have above is a relative clause. In this case "that" and "which" are basically interchangeable.

With the two other uses of "that" "which" is not acceptable.

Use 1) Paraphrasing. "That" is used whenever a quotation is not direct. Instead of saying, "He said, "she is coming home." on the GMAT they paraphrase, "He said that she is coming home."

Use 2) Distributing a concept. It is not proper to say "His courage is like a lion." "You must say his courage is like that of a lion."

You will notice that "which" cannot be used in either of the above circumstances. So this is the real difference between the two. You will not really be tested with options that make you decide between that and which, rather the choice will be between "that" and nothing.

Here is an example from the Veritas Sentence Correction 1 book. Incorrect: "The police found the witnesses were suspicious of strangers" Correct: "The police found that the witnesses were suspicious of strangers."