Why did French see himself as Homer in the mirror?

There is no explicit answer for it yet but there are many theories for it and most popular one is :

Both are same person. From bustle.com speculation on the subject:

French & Homer Are Different Versions Of The Same Person

When French is sneaking around Prairie's home in the finale, for a moment he looks at himself in the mirror and sees Homer. It could just be his mind playing tricks on him, but how would his mind know exactly what Homer looks like? The show has already talked about multiple dimensions, so is it possible that when French was looking in the mirror he was seeing a multi-dimensional reflection of himself? This would explain why French and Prairie are so drawn to each other and why he is so willing to go along with her out-there ideas.

Now that they have the 5th motion, they opened the gate and since Homer also has all 5 movements established, he is reaching out to French; as a link and channel has begun to form (across time and space which are merely physical boundaries not spiritual).

They mentioned that amnesia would be a side effect of multi-dimensional travel. Maybe Homer travelled into a different dimension, where he is Fench and not Homer, and forgot all about his past life... until it started trickling back

French plays football and Homer (the 16 yr old gets a head injury from football). Maybe French is a Homer from another dimension and he dies on the field later. He also explains all those things about her father possibly being a bad person (he drowned her first).

Also, I noticed that Homer, in the story told by OA, when he was told to seduce the older lady, he was in the shower banging his head against the hard tile, just like when young blond steve does (he says I messed up I messed up) after his dad finds out about the throat injury. All of these characters align. I think there is more to the story and how they maybe are going to die next . Not meant to just save a school from a shooting. I think he really did see himself in the mirror.

Also they don't remember most of where they go because they are gassed before they are killed over and over again.

I think the immediate implications are that there are correlations or juxtapositions between Hap's Captives and Prairie's new group that act as counterparts that work in such a way to make the movements possible for Prairie to use...

French and Homer share the idea of being young athletes, who both come to suffer head injuries, but obviously Homer's being an NDE, where French's is just a scrape from fighting with Steve.

French also has a correlation with Ranetta in the sense that his nickname is exotic and Ranetta comes from an exotic location, but Ranetta shares Prairie's extraordinary gift to play music, which solidifies the irony that Homer is used as bate, but then sleeps with her, betraying Prairie.

If one looks at Rachel, her vocal musical abilities tether her Buck, who sings in the school choir, but the story about her running away from her parents to raise her younger brother, whom tragically dies from a car accident, juxtaposes Jesse's story, as one of his parents died, the other left, and he's currently being raised [poorly] by his big sister.

Betty Broaderick-Allen or "BBA" has a cool name abbreviation like Prairie (The "OA") and both are "teachers" of sorts. She also just lost her brother Theo, who was hard to handle, but finds her brother again in the forms of Steve and perhaps Jesse.

Steve also starts to find someone, the girl from detention, where he can be more of himself with, as she is more like him. This is not unlike Prairie coming more into her own when she was held captive and finds and meets Homer.

The show's contrasts of counterparts is so beautifully sliced and isn't perfectly symmetrical.

In terms of the longer term implications, I think the series will take it's time with it.

I do think French believes he saw Homer in the mirror, making us aware that they share some things and that perhaps French plays a bigger role in terms of saving Homer at some point. But I also know that Brit Marling has a 5-season plan and that she doesn't want to simply repeat herself. So it may take a while to see the full magnitude of what this Odyssey and all it's little parts bring.