Glad you found your perfect style! Have fun with the planning :)

Just go with what you like and call it Naween style; doesn't need an architectual name.

Did you read this:
History
This house style originated in the Normandy area of France where house and barn were one building. The turret was used for storage of grain or ensilage.

Perhaps work your attached garage up to look like the haying shed or barn, so it blends in nicely?

LogBuildDreams,
I will, but I learned:
a) I really do like the style given that name,
b) it is also a bit of a nod to people on this forum who were rather cranky about my tower on my rather square house plan.

I do hope to put the arched garage doors on the garage, and maybe a dovecote (or perhaps bat house) on the garage roof spires too!

This is an American residential style usually called "French Eclectic" or "French Inspired". I haven't seen it directly associated with Normandy before. I suspect that idea is the result of naming efforts on the part of packaged pre-designed home companies which is fine but it does suggest incorrectly that this kind of house might have existed at some time in Normandy.

The style did not develop in France but here in the US between 1915 and 1945 but was out of fashion until the 60's. It is loosely based on French architectural elements from many different centuries. The most characteristic element is a steeply sloping roof that is usually hipped but there is really no limit to the variety of design element combinations.

The Normandy influence is found in the variety of mixed masonry wall materials including brick, stone and half timber from Normandy, Brittany and Medieval England. It also borrows another Medieval English element, front facing gables, adopted by another American architectural invention between the wars: the Tudor Style.

These elements (steep hipped roofs and front facing gables) are both based on late medieval European prototypes and these influences occurred together in Normandy but it was not until after the Neo-eclectic era of the 60's that the elements were used together in America.

The round tower with a conical roof was adopted from the French chateau of the Loire valley directly south of Normandy. By adding a Roman arch you could stretch the basis for the design of this eclectic style across 12 centuries and the full length of Europe. That provides a lot of ideas from which to choose.

For researching examples of these design styles the best names to use are French Eclectic (between the wars) and Neo-French Eclectic (after 1960).

A house in Normandy: