Not quite. Norman is a true Latin descendant; it starts with Late Latin grammar, then adds some sound and grammar changes. In the meantime, OP's conlang uses an English "base" grammar but replaces the native vocab with Classical Latin equivalents.

The difference is visible in cases like "id est uno vehicle accident". Norman would use ille→il and unum→(i)un, and odds are it already did so in Norman Conquest times (ditching is/ea/id, merging masculine with neuter, ditching vowels after /n/, those changes are so widespread that they were probably already in Western Late Latin).

Another difference is in the "tu est". English lacks second person conjugations, so it's using a third person one; a Norman descendant would use "tu es" (or rather "t'es") instead.

If you (or anyone here) is interested on what a British Romance language would look like, check Brithenig. It's more like a sister language to Norman than a descendant, and the conlanger added some Insular Celtic influence to spice things up, but it should give you a good idea.