A "tranche" is "a division or portion of a pool or whole," sez MW11; apparently "pool" in this context refers to finance. And "tranche" apparently has a very specific meaning in the context of bonds.
And "tranch de vie" is French for "slice of life."
I’m pretty sure that the most common usage in French is a piece of cake/pie.
And now that you mention that, I think sometime in the last couple days I’ve seen it used that way. But I’m blanking on context.
Also, your comment made me think of “trencher” (in the sense of a serving platter), and indeed it appears that “trencher” and “tranche” are etymologically related, via French (?) “trencher” meaning “to cut.”