Metro Line 10 which runs from Cluny-La Sorbonne to Gare d'Austerlitz departs every 3 to 5 minutes during the day with a journey time of 5 minutes. The RER C, in terms of journey time, is only 1 minute faster, taking a total of 4 minutes between St Michel-Notre Dame and Gare d'Austerlitz. See my article about using
Metro/RER route planners for more information on this.
Walk time from St Michel Notre Dame to Cluny La Sorbonne Metro station is about 6 minutes according to Google Maps (doesn't include time spent waiting for traffic lights).
If you just missed an RER C train, you would save 3-4 minutes at most by walking over to Cluny La Sorbonne and taking Metro Line 10. Do keep in mind that you would need a new
Metro Ticket t+ for this journey if you decided to take it. Once you leave a station, the
billet Ile-de-France from
CDG to Paris is finished and cannot be used further. If you stay within St Michel Notre Dame and simply switch from the RER B to the RER C, you can use the same billet.
I'm not sure of the difference in walking time from Metro vs. RER to the Grandes Lignes trains at Gare d'Austerlitz (I've hardly used this station), so I'm hesitant to take a guess, although the Metro/RER route planner gives the same amount of "walk time": 3 min.
I hope this helps. Best of luck,
Ben