I agree with "it doesn't matter" ... unless you only have a FEW marigold seeds, or if you (like me) love to obsess over details. Sowing orientation matters with bulbs, but hardly at all with seeds. (Most seeds?)
I forget which end the baby marigold root emerges from (the radicle).
But that isn't the whole answer, because the radicle in many seeds seems to be pre-programmed to make an 180 degree turn after it emerges.
I'd suggest putting 5-10 seeds into a folded coffee filter inside a baggie. Spritz a little water, then fold the baggie to be partly or mostly closed to hold some humidity.
Wait 5-10 days, until the radicle emerges. Now you know which end of the seed the root comes out of.
But wait another day or two to see what curlicue, if any, the radicle makes before figuring out which way is DOWN.
Now you know how to position a marigold seed so that the seed's baby root is ALREADY pointed down when it finishes whatever twist was programmed into it.
But it still doesn't matter much. It might even prefer the horizontal orientation because then the root is always 90 degrees away from "DOWN", and maybe it "expects" to have to hunt a little bit to find "DOWN".