Far from being what you are searching for, but still a workaround…

There is a book called French Grammar in Context by Margaret Jubb and Annie Rouxeville, currently to its fourth version published by Routledge.
It presents the essential French Grammar (upper-intermediate to advanced level) through literary texts and poems taken from works by renowned French authors such Camus, Zola, etc. and even Francophone writers. There are also texts taken by sources like Liberation, Le Monde Diplomatique, La Voix du Nord, Marie-Claire and Elle.

In order to give an example of presentation, chapter 3 treats the Imperfect tense (temps imparfait) through one text called: “Le dromadaire mécontent” (Contes pour enfants pas sages by Jacques Prévert). This story is in fact available online. As one sees, the author of the story employs a lot the imperfect and the authors of the book use this story to introduce various elements of the tense (usage, formation, imperfect vs perfect tense, etc.).

The book is accompanied by a useful webpage. You can find the full description of the book here.

I thought someone should at least mention the Lagarde et Michard textbook. It’s old and opinionated, but also so ubiquitous that it’s almost a part of French literature itself.

• The textbook comes in 6 volumes, sorted chronologically, with an emphasis on the historical perspective.
• This is a textbook, not an anthology per se; but every chapter comes with a selection of short, usually famous excerpts.
• We’re talking about 60+ year-old material, which is probably often incaccurate (or even biased).

Why mention it, then? Because most French literature teachers and students have been exposed to L&M to some extent (it’s a staple in Literature exams even today!)
For this reason, I think that would be a good start if you seek to get familiar with French literature — not only with the texts themselves, but also how they were taught and perceived and what was made of them for the last few decades.

A quick search on amazon.fr suggests they’re relatively easy (edit : but somewhat costly) to come by. A PDF version might be available online.

Consider this a complement to other answers with more up-to-date references 🙂