e4 Nc6
d4 d5
e5 f6
f4 Bf5
c3 Nh6
That is the Nimzowitsch defense as I have seen it most often. The chess engine gives a +0.4 for white, but this seems to be the French opening without counter option c5.
I could not find any plans thereafter, the engine suggests bishops to move on the kingside past white's pawns, but nothing else... As I see it, black has no counterplay. Why 'only' half a pawn better?
I used to play that from time to time. I also used to play the Guimard variation of the French, which is very similar. And yes, they are both pretty difficult to play. Hugh Meyers, an American master, used to play it pretty frequently, even wrote a book about it. He used to play 3...Bf5 right away, but since ...f6 chipping at the centre is a thematic move, I don't believe the change of move order is significant.
In both openings, the idea is rapid piece play against white's centre. Sorry to be so vague, but it all comes down to concrete analysis. Tricksy time. I'm not good enough to pull it off, so I have drifted off to more mainstream openings, mostly the French and Sicilian. But at a guess, I would say that half a pawn is about right. Black has worries, but is not without resources.
It's also a French defence where your bishop isn't stuck on c8. So it's rather similar to Advance Caro-Kann 1.e4 1...c6 2.d4 2...d5 where black plays go Nc6 instead of going c7-c6-c5 in 2 moves.
I think black doesn't have a lot of plans, but just developing pieces (depending on white's setup they can do it differently like (h5 with possible h4-h3 can be played before) Nh6-Nf5 (Ng4) / Nge7-Ng6, Be7 , Bf5-Bg4 in case Knight is on f3, f6-g5 / f6-fxe5 pawn breaks, Qd7-0-0-0, Qe8-Qg6. Nce7 and c5 is also possible in some positions. Black just should keep pressure in the center since their own position is also tough to crack. Once game opens, some hidden counterplay can be founded. I think going 0-0-0 can be fun.
If you analyze it properly it's a good opening unless you are a GM, I am not even talking about blitz. I think it's not played a lot because white can just go for 2.Nf3 and 2...d6 just transposes into Pirc (There are some variations with Bg4 / e5 but i don't like them) 2...e5 into classic openings (black could've played e5 on the first move), and 2...d5 into not the best version of Scandinavian.
Also because now a lot of openings which was considered dull now seem okay when you analyze it with engine. Even playing e4 Nc6 d4 d5 e5 Nb8?! is just +0,9
In the specific variation you mentioned, one idea for Black is to play Be4 followed by f5. As others said, it's like a French with an actively placed Bishop.
It's Hugh Myers, by the way, who advocated the opening (in an earlier post it is misspelled Meyers).
In his book on the Nimzowitsch, Christoph Wisnewski considers 1. e4 Nc6 2. d4 d5 3. Nc3 as an important White try as he feels 3... dxe4 too risky and instead recommends 3... e6 transposing to a rare French variation.
There are top GMs who occasionally play 1... Nc6 at fast time controls including Magnus. After 1... Nc6 2. Nf3 Magnus has tried 2... d5, 2... d6 and 2... f5. If the Nimzowitsch is good enough for him, it should be good enough for you!
