I realized that 'pointy mask' isn't really descriptive. Here's what I'm referring to.
Oddly enough, it's likely backwards. It might be too early for the beak mask. While it is iconic equipment worn by plague doctors and the plague was at its worst in the 14th century, it seems the beak mask (and the rest of the protective outfit) didn't come about until the early 17th century.
Its invention is attributed to Charles de l’Orme, chief physician to Louis XIII. Charles described his mask as (translated):
The nose [is] half a foot long, shaped like a beak, filled with perfume with only two holes, one on each side near the nostrils, but that can suffice to breathe and carry along with the air one breathes the impression of the [herbs] enclosed further along in the beak. Under the coat we wear boots made in Moroccan leather (goat leather) from the front of the breeches in smooth skin that are attached to said boots, and a short sleeved blouse in smooth skin, the bottom of which is tucked into the breeches. The hat and gloves are also made of the same skin…with spectacles over the eyes.
M. Lucenet, ‘La peste, fleau majeur’ extraits de la Bibliotheque InterUniversitaire, Paris (1994)
His date for when Assassin's creed (I assume 2, since the first game is set in 1192) is incorrect. The game covers 1477 to around 1500
Tangentially related: The developers were actually aware of the inaccuracies surrounding this, but the distinctive style of the masks ensured that it was relatively easy to spot the doctors when they were needed.
I can't tell if the game is historically correct in that these masks were worn in the time and place you are referring to, but these costumes did appear later than the Black Plague, and were used in many later outbreaks of plague in western Europe, for instance the pest of 1656 Italy.
Those masks are most likely way too early as everyone else has said, but the plague also didn't just disappear after 1352. It kept rolling around Europe very couple of centuries/decades.
http://www.preceden.com/timelines/49344-the-black-death-timeline
We mostly keep track of the big outbreaks, but there were some small flare ups as well.
