Depending on how you define 'Democracy', you could count the war of 1812 (USA vs UK) as two democracies openly fighting. Both had elected legislatures & executives at the time (although both with a heavily restricted franchise)
UK (and Canada, Australia, etc.) did declare war on Finland, and attacked a Finnish harbour[1]. While USA didn't declare war, I doubt anything would have changed if they did, since Finland was out of their reach anyway.