I just got a copy of Christophe Rico's Greek textbook Polis. I've not gotten deep into it, but here are some first impressions.
His tack is to take Koine and teach it as a modern language. This looks like a modern immersion textbook. There is some French (as Rico is French) in the book, but very little. It is mostly used in situations to explain various exercises and scattered in the back-of-book glossary, but ignorance of French probably won't detract the usefulness of the book for serious students. On the flip side, the grammar terms are in Greek. No dative case is taught here. δοτικη is what's presented.
There is a lot of comprehensible Koine Greek input, but you may find it difficult to use without a teacher. The book is designed for a class, and autodidacts were not the primary audience. Rico admits as much in the introduction of the book (or that's what I could gather from the French). To aid in learning, there is a CD to fix the sounds (Erasmian pronunciation) of Greek in the student's head.
The exercises themselves emphasize Greek in Greek and definitely avoids translation of any sort. I suspect classroom teachers would want to supplement the book with either authentic Greek or adaptations thereof.
The layout is attractive and makes the book easy to use (as opposed to the luxurious hand typesetting of 19th century books, but I digress). There are many illustrations throughout. They're cartoony, which should make the text less threatening: after all, Greek has been the domain of classicists and not reg'lar folks. More the pity, as making Koine Greek accessible could be a major aid to the faith of many Christians (to pick an example group of people who would benefit from this book). I don't know that this book is the answer for everyone, but one could do worse.
The single worst thing about the book is its availability for Americans. It cannot be had from American sources. Amazon.fr is your best bet, though overseas delivery can be slow. It is also a shade on the expensive side when compared to mass-market foreign language teach-yourself books, but quite in line with college textbook pricing.