There is no inconsistency in the paragraph. The paragraph (book decription) consistently uses Collins French Gem Grammar as the title of the book. The reason there is a capitalized the in the first sentence of the paragraph is the same reason there is a capitalized the at the start of this sentence. We capitilize the first letter of a sentence.
In your paragraph, the is not part of the book's title, it is simply the definite article used before the title. When the is not the first word of the sentence, then the is not capitilized. This is shown in the exact same paragraph. Notice the third sentence:
Have confidence: the Collins French Gem Grammar offers extensive coverage of French grammar, with a handy guide to French pronunciation.
It would help if such book descriptions used standard rules for the title of a book. The standard rule is italicize book titles, thus, Collins French Gem Grammar. If the paragraph had followed the standard rule, there would be no confusion about whether the is part of the title. The first sentence would have been
The Collins French Gem Grammar offers the learner of French extensive...
You can see the correct usage of italics to refer to a book's title at the Collins website for the book Collins Italian College Dictionary. Notice the first sentence of the description is
The HarperCollins Italian College Dictionary is the ideal dictionary for learners of Italian.
while a sentence later in the description starts:
The new edition of HarperCollins Italian College Dictionary has been completely revised...
There is no doubt as to the word the not being in the title.
As shown by your source, you will often find online bookseller sites that do not use italics when referring to book titles in the description paragraph. This is the case on bookseller wesbites from Turkey to Denmark to Ireland. They all use the description (or a portion thereof) without putting the title in italics. This may be just to keep the page looking neater. A related question is what is the actual title? It it Collins French Gem Grammar or Collins Gem French Grammar? But that question is something we can leave for another time.
As for the definite article before a proper noun, we do it all the time. Take Empire State Building.
There is the Empire State Building in New York. I am using the definite article before Empire State Building but the is not part of the building's name. When a capitlized the comes before Empire State Building it is because the is the first word of the sentence. See the wikipedia entry Empire State Building for lots of examples.
Of course, since a lot of English sentences begin with a noun phrase, a lot of sentences will begin with The (capitalized) plus Empire State Building.
You can also look at the Empire State Building official website. You can see the title of the website: The Empire State Building Experience. Since the is part of the website's or exhibit's title, the is capitalized.
But the last "tip" on the website has the following paragraph, which has three uses of the that are not at the beginning of a sentence:
You will see our uniformed personnel on the sidewalk in front of the Empire State Building. If you have any questions, please ask them, or ask inside the building. Express Pass tickets are not sold on the streets in front of the Empire State Building, only on this website or from our onsite ticket office. Other street sales agents are not employed by the Empire State Building Observatory.
The usage of a capitalized the before a proper noun is when the is the first word of a sentence, or when the is part of the title, like on the ESB website.
There are times when The is part of a title, as in the trilogy
The Lord of the Rings.
Yet, it is so common to drop the when referring to titles that I didn't even know the was part of the title until last year. And a lot of people refer to the trilogy without using the, even though The is part of the title.
(Historical note: the author did not write the books as a trilogy. He wrote six books. But two books were published together in each volume, so that is how the idea of a trilogy got started. But this is actually a mistaken trilogy.)
We can even use the before another proper noun: the name of a person.
A: Guess what?! Johnny Depp winked at me today! OMG I can die and go to heaven...
B: Are you talking about the Johnny Depp, the actor Johnny Depp...?
This is for clarification, as above. It can also be used for self-aggrandizement:
I am the George Foreman and you better not forget it.
This is a made-up example and my apologies to George Foreman if he would never use such a statement, or any similar thing, such as naming all five of his sons George.