It seems that 'Frizelle' and the Scottish surname 'Fraser' are both descendants of the same French surname.
This from Wikipedia, and see below for other Fraser information.
The exact origins of the surname 'Fraser' can not be determined with any great certainty, although there is little doubt that it came from France.
The first reputed record is that of "Frysel" (vowels were at the time often interchanged), recorded on the Battle Abbey Roll - supposedly a list of William the Conqueror's companions, preserved at Battle Abbey, on the site of his great victory over Harold. However, the authenticity of the manuscript is seriously doubted. Note: The name "Ricardus Fresle" appears in the original Latin version of the Domesday Book as a tenant-in-chief in Nottingham. Also the hamlet of Fresle exists to this very day in Haute-Normandie and can be found on Google-Earth.
The first definite record of the name in Scotland occurs in the mid-12th century as "de Fresel", "de Friselle", and "de Freseliere", and appears to be a Norman name. Although there is no known placename in France that corresponds with it, the French surname "Frézelière" or "de la Frézelière" or "Frézeau de la Frézelière", apparent in France to this day, corresponds with Scottish version in spelling and traditional area of origin - Anjou. Indeed, apparently while in exile in France Simon Fraser, 11th Lord Lovat "entered into a formal league of amnity" and "declared an alliance" with the French Marquis de la Frézelière and claimed common origin from the "les seigneurs de la Frézelière". The first annual gathering of the Clan Fraser in Canada in 1894 also recalls this connection.
Another tradition claims derivation from a Frenchman called "Pierre Fraser, Seigneur de Troile", who came to Scotland in the reign of Charlemagne to form an alliance with the mythical King Achaius. Pierre's son was then to have become thane of the Isle of Man in 814.
Yet another explanation for the surname is that it is derived from the French words fraise, meaning strawberry (the fruit), and fraisiers, strawberry plants. There is a fabled account of the Fraser coat of arms which asserts during the reign of Charles the Simple of France, a nobleman from Bourbon named Julius de Berry entertained the King with a dish of fine strawberries. De Berry was then later knighted, with the knight taking strawberry flowers as his Arms and changing his name from 'de Berry' to 'Fraiseux' or 'Frezeliere'. His direct descendants were to become the lords of Neidpath Castle, then known as Oliver. This origin has been disputed, and seen as a classic example of canting heraldry, where heraldic symbols are derived from a pun on similar sounding surname: (strawberry flowers - fraises).
Other Fraser Information
Below is from a page of information that was given to me somewhere along the way... I've had it stored away with the rest of the family tree stuff, but I have no idea where it came from.
"Clan Fraser is of Norman origin, and the bloodlines were brought to Great Britain by a knight named Frezel, from the lordship of La Frizeliere in Anjou. Legend traces the origin of the name Fraser to Jules de Berry, a tenth century French gentleman who served a plate of stawberries to King Charles the Simple and was knighted with the name 'Fraiser' (French for strawberry). In acknowledgement of this legend, the Frasers have always borne strawberry flowers in their coat of arms.
The earliest known Scottish Fraser was Gilbert de Fraser, who lived near the Borders in 1109. However the main line of Fraser developed from Sir Gilbert of Touch-Fraser, who died in 1263. Sir Laurence Abernethy was created 1st Lord Saltoun in 1445. A junior branch of the family, Fraser of Lovat, descended from Hugh Fraser, who married the Bisset heiress and obtained her lands; they are known in Gaelic as "Na Friosalaich".
Sir Simon Fraser was a supporter of Sir William Wallace (Braveheart) in the Wars of Independence against England and, just like Wallace, he was captured by the English, hanged, drawn and quartered.
Because of feuding clan issues, a great battle between the Fraser and MacDonalds was fought in 1544 on the shores of Loch Locky. The battle was known as 'The Battle of Shirts', since the combatants removed their shirts and, drenched with sweat, dust and blood, fought until there were five Frasers (of over 200 who had started the fight) and eight MacDonalds left standing.
The town of Fraserburgh in Scotland was founded by Alexander Fraser, 8th Laird of Philorth, in 1570. In 1670 the Frasers in herited the Saltoun peerage and since then Frasers have been Lords Saltoun. In 1745, the Frasers joined the doolmed forces of the Jacobites at Culloden."