The Millennium Falcon as an East Indiaman rather than a ship of the line

Would a Millennium Falcon exhibit suit a former naval town, and what historical kind of ship does the Falcon resemble?

Yes; as a ship type, the Falcon is closer to an armed merchant such as an East Indiaman, or at most a pirate vessel, than to a ship of the line.

A former naval town could reasonably display a locally built Millennium Falcon as a permanent exhibit. That cultural value is separate from naval classification. The Falcon is not the science-fiction equivalent of a ship of the line. Its mixture of cargo work, private ownership, speed, and fighting ability makes a pirate vessel or, more closely, an East Indiaman the better historical analogy.