The phrase 'the face' is correct and usable in written English.
You can use it to refer to someone's facial features (i.e. eyes, nose, mouth, cheeks, etc). For example: "She smiled, and her face lit up with joy."
Dictionary
the face
noun
The front part of the head, featuring the eyes, nose, and mouth and the surrounding area.
Exact(60)
Always the face.
The face of hockey.
What about the face?
The face of Starr.
Up in the face!
"But not the face.
He recognized the face.
In the face.
Necklines framed the face.
Signposts of the face!
It's about the face.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com