Originally Posted by
Doc Savage
Strongly suggest you call the airline and try for an earlier BUD-CDG flight.
Again, being the bearer of scheduling-bad-news, the OP is on the earliest BUD-CDG flight of the day (and the latest CDG-DTW), which is why my initial advice was possibly routing CDG-JFK/ATL/LHR/BOS-DTW instead.
There is a 6:05 am BUD-AMS on KLM as well - a slight possibility you could get on that to BUD-AMS-DTW or BUD-AMS-CDG-DTW. That would be the only option of leaving earlier.