There are many time-limited parking spaces along the street outside L.L. BEANS. The signs do not specify the days of the weeks the rules are enforced. If you think they are not enforced on Sundays or Holidays (like Labor Day) and you choose to park in those spaces, you will need to pay City of Freeport $30. There are plenty of non-street parking spaces next to L. L. BEANS. Do park at those spaces.
I have called Freeport police department to confirm that the city council make them to go out to issue many tickets on Sundays or Holidays when tourists are coming and confused. All the parking signs in New York clearly specify the rules and exceptions.
L.L. BEANS is the only thing you will want to see at Freeport. You don't want to be surprised to see the parking ticket. This is the only city in the US using this kind of trap to collect tourist money. Be warned.