You might as well call me English too (I live in Wessex after all)!
What WP seems to have forgotten to mention is who actually used those terms. I'm prepared to be shot down but I doubt there was a properly defined concept of "Western European" between say 300 to 1500 in the right hand side bit of what we now call Europe.
What you are on about is the left and right Roman Empires (my terms) and how they talked about each other.
The left lot is now nominally modern Germany and France and much besides, what was called the Holy Roman Empire. The right lot is the Byzantine Empire.
Now, your Franks were part of the left lot. The Franks were a tribal identity, cf Saxon, Angle, etc. The Franks is where la belle France gets its name (cf Frankreich, and Französisch - German names for France and French.)
I am English (by assertion and routine) but my family name says I am descended from Germans on the male line (Brits being patrilineal.) As it turns out 300 odd years ago from a Hanoverian merchant seaman and (very) loosely on my matrilineal line 500 odd years ago I have a ancestor from Padstow in Cornwall. I also have inroads from all of the home nations (England, Ireland (both), Scotland and Wales). There are also quite a few other inputs to my blood line from much further abroad.
One of my uncles is quite fastidious in his research and has many thousands of people in the DB.
We use kg most of the time for weight unless lbs and oz work better.
The m is very handy and we spell it correctly hereabouts - metre (unlike your mates in the US) but when subdivided, the cm is 2.54 too small (1 inch is 2.54 cm)
The Holy Roman Empire was a right old mish mash, just like the Pretannic Isles or Brythonic Isles or whatever.
Nowadays people are so wrapped up in modern boundaries and notions of nationalism and fail to notice that history is rather messy.
My family history has been rather well researched by my uncle who has a no nonsense approach to his findings. We have at least one mass murderer in the bloodline. An innkeeper of a pub and hostelry on Salisbury Plain at a crossroads was not a nice person. There was a chair that dumped people into the cellar where they were butchered. The whole thing has been hyped somewhat but it was 200 odd years ago. During WW1 an ancestor may have run away during a Zeppelin raid on Kent. We know he was signed up to join the army and had done basic training and was sent to a camp in Kent before despatch to France. He would have had a pass to visit relatives within reason. Anyway it gets complicated.
My point is that a simple comment like "the Franks themselves spoke a Germanic language" is a bit trite (no offense meant). We classify the Frankish language as Germanic, but then we also classify modern English as such. My name is also quite literally testament to how daft it gets.
... which is Latin for: language of the Franks - French!