The "golf bag" is hit or miss with United. I've done it about 10 times and made it free 8 and the other 2 were $250 each way. Ouch! It seems its the mood of the gate agent. Lately I bring kites and rent a board unless it's a long stay and worth the risk. I might try this flight in January too.
Usually I take AF through CDG which is easy and they seem to go for the golf bag trick. Maybe fewer french golfers so they don't know this is a ridiculous size for golf clubs.