Hola Antoine /
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As an alternative - how about considerng training with Sabena school in Brussels. Belgium people often speak French, yet in aviation they do it all in English. So, socially, you could speak French (or Dutch/Flemish) with them, but in classrooms, English is normally used. And Brussels is a mere 1 H 20' away from Paris in the TGV train...
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Funny thing is, I am a native of Brussels, grew up with French and Flemish at school, but as a kid, I did my PPL in the Brussels area, before moving to California and did most of my career in the US with airlines. While I continue to speak French often (and Spanish as I live now in Argentina), I would have a hell of a time to instruct pilots in French... all my aviation and airplane vocabulary is in English.
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Many years ago, with PanAm, I had a class of African 707 pilots who spoke French and got "designated" to teach them because I was known to speak French, yet, in the classroom, I had to mix English into my French language explanations, as there were many aeronautical wordings I did not know in French. Even had to use a dictionnary... to learn that an hydraulic actuator was... a "verin" in French...! But an "aileron" is... an aileron in French, and a pitot tube is a "tube pitot"...
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A few years ago... I flew a contract in DC-8s, and once got teamed with a French F/O and a Swiss F/E. We spoke French together, but... I was unable to do a check-lst... in French...! They laughed at me...
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Happy contrails to you