This is a good question. There is a lot of theorizing as to why there were Breton volunteers among William the Conqueror's forces. It's unlikely a commoner would have paid much concern to the royal squabbles of nobles, but, an important point needs to be made about the legitimacy of William's invasion:

He had Papal support.

David Douglas posits this in William the Conqueror: The Norman Impact Upon England:

as a result, therefore, of papal and imperial approval, and in consequence also of the conditions prevailing in France, Duke William could appeal with some confidence for volunteers from outside his duchy, and that appeal could be made in terms whereby a crude promise of plunder was buttressed by higher consideration of moral right.

his earlier wars had assured him not only of strong support from among the magnates of Brittany, but also of direct assistance from Maine

There is a very notable name that also bolsters this. Odo, Count of Penthièvre. Odo was the son of Geoffrey I, a Breton Duke, and Hawise of Normandy. Odo was the younger brother of Alan III, Conan II's father so he was further down the succession chain. Conan also had legitimate claims to the title of Duke of Normandy, which made Odo and his lineage natural allies to Duke William. When William invaded England, he was accompanied by Brian, one of Odo's sons. Alan the Red and Alan the Black, also Odo's sons, were granted land and titles in England as well as Brian.

There was a web of interwoven relations between the Normans and the Bretons so, by all accounts, the Norman invasion of Brittany was not seen as an invasion by an outside force and there was significant division within the Bretons in 1066.

It's entirely possible Conan initially enjoyed the Normans going off to England. The Anglo-Saxons under Harold Godwinson had defeated a sizeable contingent of Norwegians at the Battle of Stamford Bridge in September of 1066 so it's possible Conan was encouraged by hopes that his rivals would be ended thusly. He was potentially ridding himself of a rival claimant in Normandy and rivals in his own territory with Odo's lineage, who were all grandsons of Conan II's father, Geoffrey I.

Regardless, he didn't have long to wallow in the success of William and his Breton rivals as he was poisoned within 2 months of Hastings.

EDIT/NOTE: This should get the 11th Century tag.