For He's A Jolly Good Fellow

Would this song be in period? the short answer is YES, but there is a long answer too.

The tune has apparently a long history, with some people dating it back to the crusades adapted from tunes by Arabs in Palestine. This interpretation is now contested as the structure of the tune is more similar to Louis XIV France. At any rate, it was known in France by the 1700's as 'Malbrouck s'en va-t-en guerre' (after the Duke of Marlborough), and it was made popular by Marie Antoinette. It was so much associated with France that Beethoven used it in a symphony to celebrate a military victory over France.

The first English use of the air seems to be a satyrical song about the siege of Gibraltar, "D'Artois returns from Spain", written about 1782.

It soon became popular in England after this, and was used chiefly as an instrumental piece for violin or flute, and finally became a teaching piece on the harpsichord. About 1830, however, somebody used the melody for the words, "We Won't Go Home Till Morning", second verse "For He's A Jolly Good Fellow", and from that time on the melody has spread all over the world.

-- From Grove's Dictionary of Music and Musicians.

Wikipedia notes that the song has different American and British lyrics:

American lyrics
For he's a jolly good fellow, for he's a jolly good fellow
For he's a jolly good fellow (pause), which nobody can deny
Which nobody can deny, which nobody can deny
For he's a jolly good fellow (pause), which nobody can deny

British and Australian lyrics
For he's a jolly good fellow, for he's a jolly good fellow
For he's a jolly good fellow (pause), and so say all of us
And so say all of us, and so say all of us
For he's a jolly good fellow, for he's a jolly good fellow
For he's a jolly good fellow (pause), and so say all of us