Learn French: Il a les mêmes traits physiques que ton sosie. - He has the same physical features as your lookalike.

In French, when you use le/la/les même(s) (the same) to compare things, it is always followed by que to mean "as". While comme often means "like" or "as" in other contexts, you cannot use it after même. So, "the same... as" is always le/la/les même(s)... que.

Why is it les mêmes with an "s"?

Même acts as an adjective here, modifying traits (features). Since traits is plural, même must also take an s to agree with it, and we use the plural definite article les.

Why does mêmes go before the noun, but physiques goes after it?

Most descriptive adjectives, like physiques, go after the noun in French. However, a small group of common adjectives go before the noun. Même is one of these special adjectives that goes before the noun it modifies, which is why it sits directly in front of traits.

What if the "lookalike" is a woman? Would it be ta sosie?

No, the word sosie (lookalike or doppelgänger) is always a masculine noun (un sosie), regardless of the actual person's gender. So even if you are talking about a woman's lookalike, it remains ton sosie.