"Country + Market" & "Nationality + Market"
Solution 1:
Yes “Japanese market” is correct. But not because “Japanese” as a descriptor of a type of person (nationality) but simply from the meaning ‘of Japan’ (adjective).
To see the distinction more clearly, it would be “Finnish market”, not “Finn market”.
In fact, “Japan market” is more of a shorthand that a rather technical writer (for a finance mag, for example) might want to use.