Here is a review of the times and locations of Extraordinary Form (EF) Masses in Maine, as of April, 2018. Please note: All the times and locations are on the sidebar as well as this post.
The St. Gregory the Great Latin Mass Chaplaincy sponsors two EF's every Sunday. The first is at 8:30 AM in the upstairs (main sanctuary) of the Basilica of Sts. Peter and Paul, 122 Ash Street, Lewiston.
The second is at Noon, in the side chapel of the Cathedral of the Immaculate Conception, 307 Congress Street, Portland
In addition, on First Saturdays at 7 AM there is a Mass, also at Saints Peter and Paul Basilica 122 Ash Street, Lewiston, but this one is in the downstairs chapel (not upstairs in the main sanctuary). This one may be discontinued later in the spring/summer of 2018 due to priest transfer, but at least as of now (April 2018) it is still going.
Also, Third Sundays 9:15am"Missa Cantata"St. Anthony Franciscan Monastery28 Beach Avenue, Kennebunk (see sidebar for contact information; sorry, no pictures).
Other EF's pop up from time to time as "one offs", keep it tuned here for dates and times.