In tracing the genealogy of the Watertown Coolidge name, I found changes of spellings. I finally got back to Thomas de Colyne who died around 1495. The name looks French, but these people were Anglo-Saxon. Why did these A-S add the de? Were they trying to sound French?

The "de" seen next to some English surnames in this period is a "descriptive particle". It is not exactly part of the name as we would think of it today, rather, it signifies something important about the surname - either that the person with that surname is from a place with that name (a "locative" surname), or that they are descended from a person with that name (a "patronymic" surname). Someone called de Colyne is likely either from a place named Colyne or descended from a man with the given name Colyne. In spoken English it may or may not have been omitted or substituted with "of" or "a", and over time there was a tendency to drop the particle from written records of names. "Legal French" or Latin were used in many documents during this period, which could lead to the Latinate equivalent particle "de" being used when recording the name of an individual known to have a locative or patronymic surname, independent of their heritage.

Remember, William the Conqueror and his knights were French-speaking Normans and the nobility continued to speak French as a first language for centuries. A weird modified French persisted in English courts of law and legal documents until it was finally abolished in the early 18th century. In 1495 the King of England, Henry VII, also held the territory of Calais in France and claimed to be King of France as part of his official title. It is common to see French or Latin influence in how "English" names are rendered before the 16th Century, because the people with power in society came from a French influenced milieu. Henry VII was actually a pretty important part of changing this, but that's another story.

The presence of a descriptive particle is sometimes claimed to signify a "personal surname" that was only in use to describe an individual with no formal family surname (e.g Smith, 1864, p.12-13 ), but this is not definitive.

It's tempting to think that a record of someone's name in a document is indicative of how they themselves would have spelled or pronounced their name ("trying to sound French" as you say.) But without other context it can only be taken to reflect how the writer thought it was appropriate to spell the name in a document of that type.

In some languages descriptive particle are taken as indicators of nobility (e.g. von/van in German) but this is rarely or only incidentally the case for English surnames.