My Peugeot mixte is 56 cm and I am also 5'7 (and a woman) and it fits me just fine.
Since you are on a tight budget, I will say that you might want to be a little wary of old French bikes. For instance, after I bought mine I discovered that it had an AVA "death stem" (very typical on these French bikes - high or lower end) and it is recommended that they be replaced due to failure. Of course, older French components also have different sizing making it difficult to find replacements on the cheap.
My husband is now calling my $50 Pug "the moneypit" in a not so affectionate way.