7:10 AM PT -- According to Barnstable Police, LaCroix, who police discovered sitting on a couch and reading a book, told police he entered through an unlocked door. LaCroix also said he had a gift for Perry and was also there to see ... John F. Kennedy.
Cops say that after talking to LaCroix for a few minutes, they realized he "was detached from reality."
A scary moment for the Kennedys at the famed Hyannis Port compound ... a crazy guy entered the house looking for Katy Perry and hung with the clueless 16-year-old grandson of Ted Kennedy.
Barnstable Police tell TMZ ... there was no sign of forced entry. At around 6:30 Tuesday night ... 53-year-old James LaCroix just walked inside and started cooking dinner.
Ted Kennedy Jr. -- who was in Connecticut -- called the home just after 9 PM to check on his teenage son. The intruder answered and the panicked dad called the cops.
When cops arrived they found LaCroix -- still in the kitchen -- and he said he was there looking for Katy Perry.
Cops say Kennedy's son came home in the evening and ran into LaCroix ... but he thought LaCroix was just a house guest.
LaCroix was arrested and charged with breaking and entering.
In 2 weeks the house will be filled with Kennedys ... Cheryl Hines and Robert Kennedy Jr. will tie the knot there.
Hyannisnews.com shot video of LaCroix being led out of the home.