FT simply means that if the some of values (say the forcé of gravity) would have been slightly different, life would have been impossible. Which is not controversial scientists generally agree with this premise.
OK, but then how does that play into your argument?
For example, using the same definition, the universe is fine tuned to produce planets. You focus on life, when the argument works for *any* property of the universe that could be slightly different.
So, the universe is fine tuned (according to this definition) to produce iron atoms.
This is either design, chance, or necessity.
Hmm....what does this mean and is it a valid trichotomy? Design usually means 'an intelligent agent intended the event to happen as it did'. Necessity, on the other hand, says that it couldn't be other than it is. Chance, though, suggests a randomness that is not guaranteed by the exclusion of the previous two. So, if the laws of nature are not necessary and are also not the result of an intelligent agent, it is still possible they come about in an orderly way that is MOSTLY determined.
In this context, necessity would mean that it is impossible for the constants to be other than they are. Frankly, we do not know if this is the case or not. It is also possible that the values we see are the result of natural laws that we do not know about that 'push' the constants to the values we have. We simply do not know what determines the values of those constant, if anything.
But, let's turn your trichotomy around: is it clear that something is either necessary, happens according to chance (probabilities), or is designed? I don't think so. For example, an acorn falling from a tree with nobody around. The falling of the acorn would not be necessary. it would not be due to chance (since it is governed by natural laws), nor would it be by any design (since no intelligence is in the picture at all). All that is required is that there be variance in how the natural laws work from situation to situation and we get a fourth category of possibilities. The leap to design seems very premature in this argument.
Then, you claim that the values of the constants are not due to chance or to necessity. How do you know that? And, given those are NOT the only possibilities, how do you know they aren't the result of a combination of natural laws with some probabilistic flavor but also some law-like aspects?
Now, *if* you can show those are the only three possibilities (not done, and likely to be false), and if you can exclude two of the three (also not done and likely to be impossible), then you could make the conclusion you want.
But those are very big 'if' statements. And you still have to make an argument that gets past iron atoms.