There is a new database devoted to 3...h6 at Modern-chess:
French Defense for Black - 3..h6 against the Tarrasch Variation by GM Baadur Jobava GM Pier Luigi Basso, January 14, 2026. "If you're tired of passive equality in the Tarrasch, this course offers something better: initiative, clarity, and a real fight"
This has also been seen from the White side at Modern-chess:
Positional Repertoire against the French Updated
GM Renier Castellanos December 11, 2017
3.Nd2 - Strategic Repertoire against the French Defense
IM Dejan Marjanovic September 4, 2024
Going back further, another source is John Watson's Play the French (4th Edition, 2012). This variation has been analyzed many times at ChessPublishing.
A key position can be reached after:
1. e4 e6 2. d4 d5 3. Nd2
h6 4. Ngf3 Nf6 5. e5 Nfd7 6. Bd3 c5 7. c3 Nc6 8. O-O g5
or
1. e4 e6 2. d4 d5 3. Nd2
Nf6 4. e5 Nfd7 5. Bd3 c5 6. c3 Nc6 7. Ngf3 h6 8. O-O g5
Black should not assume that he will reach this position as white has significant ways to vary.
From this position, 9.dxc5 has been played most often, followed by 9.h3. Marjanovic recommends 9h3. Castellanos recommends 9b3.