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No, the shape and most of the composition. The French are just entitled enough to pretend it is theirs. Western European nations seem to like doing this.
What you are talking about is kipferl which is definitely Austrian. But someone took that and made it into something new using yeast-leavened laminated dough, called it croissant, and where they did that was 100% in Paris, France. There is no doubt about it because it happened recently enough. They are absolutely not the same end product and I would be outraged if someone served me half-moon shaped bread roll, which is what the Austrian thing is, while trying to pass it off as a croissant.