Wouldn't Italy have cared more about Trentino, Trieste, and Fiume than about Ethiopia, though?
Maybe but France didn't hold those so France couldn't bargain for it!
Couldn't Italy have conquered Ethiopia in 1896 with better generals, though?
Sure, perhaps, it wasn't out of reach for a Great Power with the will and the mean. I'm not that knowledgeable about the Italian tentative but my point about France was that it would be long and bloody. On one side, you have very bad fighting conditions but on the other, the guys on the other side actually know by which end to hold the rifle.
Italy needed that for their national mythos: they wanted to show the World (i.e. Europe) they mattered. France here doesn't have that need. Way easier to strangle them economically if needed
Also, couldn't Ethiopia hold value for France by allowing France to build a transcontinental railroad across Africa from east to west if it will successfully conquer Ethiopia?
That would indeed have value but not enough to justify a war over it. It would also be a massive project which would have troubles getting funded. I encourage you to look at the thread "An Empire's folly" about the Transsaharian railway, it will give you a good idea of the difficulties

It was WAY more strategic and yet never got funded!
Doesn't France itself have enough funds for this, though?
Can you please elaborate on the part about the difficulty in funding Tonkin?
Yes and no. If you look at a balance sheet, yes, of course France was rich enough to pay for it, and more over. But each of these wars has to be approved, and funded through a vote at the Assemblée Nationale, which is fairly reluctant about that whole "let's colonise the world!" thing.
People on the left thought it disgusting and a perversion of Republican values, people on the right thought it a waste of men and money that could be better spent preparing the inevitable war of revanche against Germany. All agreed it was a bloody waste of money.
Jules Ferry, the chief of government, was famous for his back-handed funding tactics. Basically it went like this.
"Jules, you can't go colonise more places.
-Ok.
*Some lieutenant somewhere trips over a stone*
-Oh no! France is under attack, we must fund this expedition, they are killing our boys!
-Ah fek it, but that's the last time Jules!"
It lasted a while until the Franco-Chinese war of 1885 and the Tonkin Affair. Basically, the French took a city in North Vietnam but then had to retreat, losing a few men. The general sent a telegram saying he needed urgent reinforcements not to lose the war.
The papers saw it and went mad about it. It exemplified that "waste of money and men" I was talking about and led to the downfall of the Ferry government.
In the end, it wasn't that bad: he lost 70 men and 200 wounded retreating from a 25000 strong Chinese army in an awful region (mountains+jungle+malaria+hostile natives+fairly well equipped and very pissed adversary)