The following flag is worn by Princess Isabella when she meets William Wallace.
Technically, it's not a flag it's a surcoat. It represents the coats of arms of her family. In heraldic terms, the display of these arms are known as impalement. In this case, the arms on the dexter side (her right) represent the arms of her husband, Edward II (the coat of arms of England) and on the sinister side (her left) those of her family (the coat of arms of France). The blue band on the Arms of England is known as a label and designates the oldest son of the king (aka the Prince of Wales).
As noted in the comments, the historic accuracy of the garment worn in the film seems questionable. As the Wikipedia article notes, Isabella was only nine/ten years old when Wallace died (and not the young woman portrayed in the film). She married Edward II in 1308, by which time Edward was already King of England. Therefore his coat of arms should no longer bear the label it has in the image.
As killing time says in his answer, Princess Isabella (called "The She Wolf of France" by historians centuries later) is wearing a surcoat with the coats of arms of her husband Prince Edward of Wales and herself (or the coat of arms of her father King Philip IV the (Un) Fair of France and Navarre).
Putting two or more different coats of arms together on the same shield, cartouche, seal, banner, surcoat, etc., etc., etc., is called marshaling. Forms of marshaling include quartering, dimidiation, and impalement (no doubt Dracula's favorite form of marshaling).
It is customary for the coat of arms of a married couple (if they are both armigerous) to be marshaled by impalement. But I don't know when that practice started, so I can't say if Edward's and Isabella's arms would have been impaled in 1298, 1305,or 1308.
So what is Princess Isabella (c. 1295-1358) doing wearing a surcoat? Knights and warriors wore surcoats, and later jurpons, and later tabards, either plain or emblazoned with their coats of arms, over their armor, whether chain mail or plate armor, in battle, on campaign, and in tournaments.
A lady, princess, or queen could and often did accompany her husband, son, father, or other male relative on a campaign, but would not be expected to fight and so would not wear armor very often if at all, and so would not wear a surcoat, jurpon, or tabard over armor very often if at all.
Of course a lady, princess, or queen might wear a surcoat, jurpon, or tabard emblazoned with her coat of arms over her civilian clothes, instead of over armor, on various occasions, saying that she wanted to wear her coat of arms even if she wasn't a warrior, and if she did, more power to her.
As a matter of fact, there is some evidence for some medieval persons, both male and female, wearing civilian robes and gowns emblazoned with their coats of arms, which we can hope was a very widespread practice.
The Wikipedia article on Isabella herself has several medieval illustrations depicting that practice.
This picture is said to date from 1315:
Source: Wikimedia Commons
Philip IV and his sons wear robes with the French coat of arms - one has a label for difference. Isabella herself wears a robe that on inspection turns out have have the English coat of arms, red with three gold lions passant gardent. Which means the man with a similar robe and a crown should be her husband King Edward II and not her brother Louis.
This "near contemporary" illustration
Source: Wikimedia Commons
shows boy king Edward III of England doing homage for Aquitaine to King Charles IV of France in 1325. Charles wears a robe with the French coat of arms, Edward wears a robe with the English coat of arms, and Isabella wears a sort of a robe with the English and French arms impaled.
So therefore there is some evidence for males and females wearing coats of arms on their coats and other civilian, peacetime, garments.