In the third movement Ludwig van Beethoven's Piano Sonata in C minor, Op 13 we find a use of an augmented-sixth chord. At this point in the movement the piece is in Eb Major, and in measure 46 we find a French augmented-sixth. It works very much as a chromatic passing chord, as it passes from Ab-A-Bb in the soprano and from C-Cb-Bb in the bass. It comes from a IV chord and resolves as we expect to a V chord.
If I were performing the piece, I would push through this chord and foreshadow the crescendo that comes a few measures later. The V chord seems like a very important chord in the excerpt and I think that the few measures before it, starting with repeating quarters, seem to build through the French 6th to the V.
Also, in measures 49-50 there is a chord that some might mistake for an augmented-sixth chord. There is a B, the same as Cb, and an Eb, but it lacks the A natural needed to complete the augmented sixth. Therefore it is not an augmented-sixth chord.