I had a look here but I can't see St Malo on the map
Yes you'll have to pay for your bike spot, but only if your trip includes a TGV segment.
The map you're showing is for intercités which is another type of train and does not seem to run the route you want. If you search on the SNCF website with your itinerary you'll see you're allowed a free spot for the bike on the segment from Saint-Malo to Rennes, but you'll have to pay on the TGV from Rennes to Quimper. If you're taking the TGV you need to reserve a spot for your bike, the reservation costs 10 Euros.
There's another, slightly longer trip, that doesn't take the TGV where you'll have a free spot all the way to Quimper (as long as you're on a TER). While travelling on a TER you don't need to reserve a spot for your bike, but you can tick the "Travelling with a bike" while reserving your ticket.
Il est possible de réserver votre billet et voyager avec votre vélo en cochant la case "je voyage avec mon vélo". [...] L'embarquement du vélo non démonté est gratuit sur les TER et certains INTERCITÉS sans réservation obligatoire. Cet embarquement est alors autorisé dans la limite des places disponibles.