How much time should we allow to get from a hotel in the Montparnasse neighborhood to the Chateau de Versailles? We have a 9:30 AM tour. Is the traffic very congested at that time of day? Is it better to take a taxi or book a hired car at a set rate? If booking a car is better, can you please recommend a good company? I know trains are also a good option, but for a few reasons our family has decided to take a taxi/car this time.
My guess is that without traffic, the trip will be around 50 euros. With morning rush hour traffic, who knows, but maybe around 80 euros. If you are going on a weekday, expect traffic congestion and leave by 8 AM. I have a thing against 9:30 AM appointments because unless they are very close by, they usually force you to leave during rush hour and deal with rush hour traffic.
How many in your family? Remember that cabs in Paris aren't large sedans. Your hotel could arrange a cab or you could use Über and it would cost $45-50. Since you're leaving at the height of rush hour, I would allow no less than an hour to an hour and a half. Reconsider taking the RER from Gare Montparnasse - a fifteen minute trip for about $3 per pax.
For 1 to 4 passengers, the rate would be approximately 50 EU and would take 45 - 60 minutes, depending on traffic.
If there are more than 4 passengers, each will pay an additional 4 EU. There is no charge for baggage, and rates also apply to infant children.
G7 Taxis is a reputable company, with English-speaking operators, or the option to book your trip in advance online. In this case, there will be a reservation or dispatch fee of 7 EU added to the meter. You will need to provide the number of passengers and your address, as well as a phone number, so the dispatcher can alert you by SMS to the model and color of the taxi which will pick you up. Be waiting on the sidewalk a few minutes before scheduled pick-up time. If you know the actual time you will be leaving Versailles, you can book a round-trip. Child seats are available at no charge with advance notice, and if you require a vehicle which can accommodate people with mobility issues, those are also available. https://www.g7.fr/en/
I would take the train because it is fast, cheap and doesn't get held up in traffic. If your family is larger than 4 people then you could order a larger cab that would accommodate 5 or 6. The rates on those are whatever the meter shows plus an extra fee for the 4-6 person.
Experienced visitors to Paris and those who use public transport on a daily basis might think getting a group of people to Versailles would be a piece of cake, but it doesn't sound as if this is the case for the OP. Trains to Versailles are hot and crowded, especially in the Summer.
There's nothing wrong with taking a regular taxi, since that's what they've already decided they want to do.
Booking a reliable private car service will cost a whole lot more than the taxi will, but if the OP would like to be assured that someone would be there to pick them up at a particular time and place, it's something to consider.