I should respond here, since the recommendation for Schulz and Griesbach probably came from me originally, one way or another.
I didn't learn German using it (I found it after I was already fairly fluent in German). I continue to believe that it's a useful textbook for a particular group of self-taught learners, but it won't suit everyone's needs.
It is and it isn't like Lingua Latina. It's not a set of connected readings which allow the learner to deduce meaning from context. It's in part a fairly traditional grammar-and-drills style textbook which is written entirely in German and includes simple readings that introduce and reinforce vocabulary at the beginning of each chapter. The exercises do a wonderful job illustrating how German cases and syntax work and they give chances to practice it in a very controlled, guided manner.
It was written in the 50s or 60s and hasn't been updated substantially since then. So -- you're not going to find information on contemporary German idiom, dialogues that will prepare you for booking a hotel or doing business in Germany, or a lot of relevant cultural information. If you like your language teaching to be embedded in a realistic communicative context, this isn't the book for you. The vocabulary is deliberately limited and the introduction of material is slow and systematic.
If you're particularly interested in acquiring reading competence in German and like to be able to see how all the grammar fits together rather than being presented with a bunch of idiomatic expressions which are useful but contain all sorts of grammar that you haven't yet learned, I think this is probably an excellent textbook.
There's a book by Hannelore and William Crossgrove called "A Graded German Reader" which is quite good for learning and introducing vocabulary from a very beginning level. I absolutely recommend it regardless of your ultimate goals.
At a more advanced level (i.e., for people who already have a solid foundation in grammar and basic vocabulary), there's "Aus deutscher Geschichte" by Werner Haas and a series of "Cultural Graded Readers" mostly by C.R. Goedsche focusing on the lives of famous Germans. These are all long out of print, but it should be possible to find relatively inexpensive used copies.
There may be more recent readers aimed at beginning-intermediate level learners, I'm afraid I'm not widely familiar with the current pedagogical material as I'm not the intended audience and haven't been for a long time.
For French, I like the (again out-of-print -- notice a trend here?) book "Beginning French: A Cultural Approach" by Hendrix and Meiden. It's not really Lingua Latina style at all, but it does have substantial readings and a systematic approach which I like.
There's also the "Easy French Reader" by R. de Roussy de Sales (in print and fairly inexpensive) -- the beginning part of this does come pretty close to Lingua Latina, in terms of being able to read and understand it & learn vocabulary from context without any previous knowledge of the language, although it helps coming from an English-speaking context as many of the words will look somewhat familiar. It's just a reader, there's not really a formal grammar component.
I suspect in the end, of the courses currently widely available, Assimil probably comes closest to the "inductive" method of Lingua Latina. (I assume this is the appeal for most people -- my needs and learning style are somewhat idiosyncratic) Whether you're willing to pay the price tag that goes with it you will have to decide for yourself, of course.
IPHIGENIE: Kann uns zum Vaterland die Fremde werden?
ARKAS: Und dir ist fremd das Vaterland geworden.
IPHIGENIE: Das ist's, warum mein blutend Herz nicht heilt.
(Goethe, Iphigenie auf Tauris)