Really? Although the power of the French crown was extending, with the decline of feudalism it was not until Abbott Sugers was able to remedy this with introduction of liege homage that the King of the Franks became the King of France and the Duchies and large counties of France began to properly fall under his dominion and control. Even then you had the allodial states of Gascony and the areas around Bordeaux and the Medoc out of his dominion. The counts of Almanac down in Languidoc were always a law unto themselves, as were the erstwhile English allies of the Dukes of Britanny. Indeed, the English crown held dominions over Aquitaine/Gascony. So I’d refute your comment about England being a bit of France.
To take the above point further, England didn’t become ‘a bit of France’. I think you’re misunderstanding the implications of the Treaty of Paris 1259 and the very serious (and unbelievable on the English part, unnoticed!) clause in regards to Liege Homage of the English monarch; in essence the coach and horses that the French lawyers were able to place in the treaty without the English clergy picking up on.
Edward I saw himself as an English man, much in the same way his (incredibly lairy) grandson and great grandson would also. They were French only in their styles in so much as they mirrored Phillip II; i.e. they were all aggressive hardmen.
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