Yes, there is! For most people, head to the Eurostar information desk on the right of the departures area. For those with Carte Blanche or Business Premier, head to the information desk downstairs in the lounge by the entrance.
Let the staff there know which train you are on that was delayed, and that you have onward connections. Give them your onward train tickets. They will hunt around in the draws for the magic CIV stamp, then stamp your onward tickets. They should also write a note about the delay on the back for the SNCF staff.
On arrival in Paris, for trains with compulsory reservations you should see ticket off staff in France, or otherwise staff on the French train before boarding to get new seats. For non-reservation trains, your tickets should now be fine.
Your stamped tickets should be something like these: