This is an interesting question - the answer is, it varied.

Much of this depends on how much the king was portrayed in public art such as statues and paintings that were viewable by the public. Less ambitious kings might have had a few statues or paintings made of them, primarily for private use, making it less likely they'd be recognized.

French kings were well known for the laying on of hands once every year, which was supposed to cure Scrofula. During these ceremonies thousands of people would see the king close up. King Louis XIV, who reigned for an absurdly long time, like met a small, but not insignificant portion of the realm this way (maybe 2%). In addition to this, he had a huge amount of public depiction - in statues and in paintings. While he would have likely been easily recognized, he was an outlier. Most kings would probably not have been recognizable in this way.

I'd recommend a general history of European monarchs, or if you're more interested in the idea of depicting royalty check out Burke's The Fabrication of King Louis.

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