Taxi G7 is the largest taxi dispatcher in Paris. Most taxis you find at the official taxi queue are Taxis G7. There is absolutely no need to arrange in advance for taxi service. Taxis are plentiful and can easily carry up to 7 passengers and their luggage.
Shuttle services are consistently unreliable in Paris and I would particularly avoid any service established basically for tourists, i.e. any using the English word shuttle in their name.
However, it appears you are looking for more than just the basic service. Some hotels (typically 5 star) offer an option which will pick you up at baggage claim and escort you through customs and onto their awaiting car service. I would definitely contact the hotelīs concierge, but short of that, I have heard that Blacklane does a good job.