Aha! According to Google Maps, there are some options for making this journey today that will use the Paris Metro, but you would still have to change metro line

Aha! According to Google Maps, there are some options for making this journey today that will use the Paris Metro, but you would still have to change metro lines en route between Gare de Lyon and Gare Montparnasse (the "one change" that littlestymaar mentioned) It's possible that these options already existed in 2006 but were complicated or inconvenient enough that no one or no web site suggested them to you.