A few things have changed since the '60s, including what we call "moderately priced." Could you perhaps have been thinking of La Bonne Soupe? It's on 55th, not 56th, and although it's been around a long time, I can't say if it's been there for 50 years.
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www.labonnesoupe.com]
The only other French restaurant that's possibly been around that long is La Grenouille, which was never moderately priced in any decade! I believe it's now the last of the haute French restaurants.
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www.la-grenouille.com]