In the 19th century they used to mark the stress in spelling from time to time, but IME not with any great degree of consistency (so you probably shouldn't put too much stock in whether the mark in question is e.g. a grave or an acute). Occasionally it might be useful to indicate that, for the sake of meter, the poet wants you to place the stress on some other syllable than where it would normally go. Much of the time, however, the accent mark is placed exactly where everyone would expect it anyway, so it doesn't convey any useful information. Thus e.g. in zna, as you pointed out, there isn't really any other way to pronounce it than zná, so the accent mark is not very useful there.
Another reason for accent marks might be instances where several words have the same spelling but differ in the stress, so the mark could be used to disambiguate (e.g. sívi the adjective vs. siví the verb; or kót the noun vs. kot (unaccented) the conjunction) - but in practice this is mostly unnecessary since the context makes it clear which word is intended.
I wouldn't expect them to ever try to explicitly indicate tones except perhaps in books specifically about grammar or linguistics - I don't think that, for most of the 19th century, they even had any generally agreed-upon convention on what symbols to use for tones, and even now when such conventions exist the general public can hardly be expected to be sufficiently well aware of them, so books aimed at the general public don't use them.
In the case of his name, it is pronounced with an open (and short) e rather than a close and long one, so Francè gives an accurate idea of the pronunciation while Francé looks actively misleading. The e does turn into a close one in other cases, however (e.g. genitive Francéta).
About treti, you're right - basically that verb can be conjugated in two different ways: trèm, trèš etc. or tárem, táreš etc. The former one is more likely to be used for actual physical crushing (trem orehe), the second one for the figurative one (kaj te tare?)