My fiance and I will be in Paris on January 7th, and need are flying to Barcelona that day. Our Vueling flight is at 9:40 am.

We will be staying near Disneyland Paris, so the earliest train would get us to the airport at 8 am, which is 1 hour 40 minutes before our flight. We each have a carry on bag, so nothing to check

Is this early enough to arrive for our flight, or should we be taking an Uber from Chessy to Charles De Gaulle?
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Personally, I think that is cutting it too close.

What does your airline say? Most airlines suggest 3 hours for international flights (and probably for good reason).

That is enough time for a Schengen flight.

That’s sufficient time, but expect weekend strikes by cabin staff against Vueling until the end of January, which includes your purposed travel date.

I would plan to be there an hour earlier than you are thinking. You'll probably be OK, but too much can go wrong.