My family of 4 have a train from Gare Lyon departing at 7:58AM. What is the best way for us (with luggage) to get to the station from our hotel on Rue Cler?
A taxi or shuttle would be the easiest and quickest. Ask the hotel to arrange it for you prior to your trip.
If you're packing light enough to easily schlepp your bags, you could take Metro line 8 from either Ecole Militaire or La Tour Maubourg to Madeleine, transfer to Metro line 14, and take it to Gare de Lyon. (Under 20 minutes, including transfer time.)
Or if you don't want to go up and down the stairs at Metro stations, you could take bus #87 directly from Ecole Militaire to Gare de Lyon (a 20-minute ride).
Thanks for your prompt replies.