The French is the same as 6-row Stradella, but instead of having 2bass+4chords, you have 3b+3c. You drop the Dim chord row and gain a minor third bass row instead. A huge amount of blues/rock/rock'n'roll riffs become very easily playable with the bass line.
It's very easy to switch between the two systems - to go from French to Stradella, you just shift your fingers 1 row up. From Stradella to French you shift them 1 row down (but you no longer have easy minor third bass access). So no re-learning required at all, unless you make heavy use of dim chords on the Stradella.
I'll drop you a message about the book.
In regard to the right hand side B system,
It's a very easy, "universal" system that you use as a base for playing everything, and it keeps your hand in comfortable & relaxed position. C row & D row fingering are reasonably similar (unlike the 3-row keyboard where the 3 row fingerings are wildly different), and you only alter your fingerings if there's a good reason for it (you'll figure it out yourself, as everything is very intuitive).
The base for the fingerings is shown in a pic below. Note: The row numbering is upside-down, i.e. in the picture,
the bottom row (5) is the outer ( further away from the bellows) row of your keyboard (despite being marked as "5" - I think most people will call this row "1").
Numbers next to notes refer to fingers (1 = thumb; 5 = pinkie). A "-" after the number refers to the first additional row (confusingly marked as row 2 in the diagram), and a "+" refers to the second additional row (i.e. closest to the bellows, confusingly marked as 1 on the diagram). If there's no + or - after the finger number, you just play it on your main 3 rows.
The hand position is always perpendicular to the keyboard (it changes angle slightly as you go up & down the range, but there's no position changes to learn like you'd do on a 3-row keyboard).
Obviously, any key from the "G" row can be fingered with either "C" or "D" pattern - you've got a lot of choice here.
Apart from the main idea shown below, there's about 20 pages of diagrams for different scales & arpeggios, but they tend to follow the same concept as the major scale: similar-ish standard patterns for C&D and relaxed hand position.
You can see main pattern from the C scale: you play C-D-E-F with fingers 1-2-3-4, then you shift the hand to play G-A-B-C in exactly the same 4-finger manner (1-2-3-4), unless you intend to continue playing the scale an octave higher. In which case you need to finger 1-2-3-1, so you are starting with a thumb on the C for the new scale run.
The D row pattern is the second one you need to learn. Playing D-E-F# with 1-2-3, then shifting your hand to play G-A-B-C# with 1-2-3-4. The final D is played with a pinkie or with a thumb if you are continuing to play the scale an octave higher.
Apologies if my explanations are rubbish - the system itself is very straightforward.
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