Classical Theism

Just read essences into laws whenever "laws" shows up. The laws are grounded in the essences of things, so the argument instead becomes "why do we get these things, whose powers are life-permitting, instead of these other things, whose powers and activities would not be life-permitting?". Literally nothing changes. We just have a grounding for the laws now, but what the FT argument is concerned with is with the probability of these laws being the case - if we accept a thomistic view, then probability issue is simply moved to the existence of the particular lawmakers/essences which ground the laws. So, nothing changes, basically.

Except if a weird objection can be made. I think someone could perhaps object that there could be no two essences that were exactly alike in every aspect except for A having a difference X and B having a difference Y. The differences would have to follow from the rest of the essence, so as a result there could perhaps be no different values for constants and so on.
But I think this would actually be a very bad objection, since 1) the difference could also come from an external cause, and not from the essence itself. Human beings for example, I believe, are only rational because God decided to give us rationality; the power of a rational intellect does not follow from the rest of our bodily powers, obviously. Only in a First Cause that is necessary by itself would it be the case that every essential property would have to be intimately connected and not have any external cause; 2) it seems, in any case, that there is no necessary connection between the laws and the constants having the specific values that they do; 3) it also seems that it should be possible for there to be different laws like that, or at least other substances that are very alike but which have some differences, such as a water-like substance that boils at 101 C, etc.

So I think thomism makes no difference whatsoever to the fine tuning argument.