I'm sure there is a great deal of artistic license there.
That Me 109 would have been gone long before that P-51 got that close.
And while absolutely not definitive, Paris was declared an "open city", meaning that there would be no hostilities there. No defense. How and if that would apply to fighters in hot pursuit I don't know, but it does leave how much military activity would take place open to question.
I have no doubt a bunch of people flew under the Eiffel Tower, I just suspect this scene.