I went from Conques to Moissac last year. It is possible, but it does involve several changes of transport.
It was a school day when I was leaving Conques, so I was able to take the early morning school bus that goes to Rodez. It doesn't take a direct, fast route to Rodez, as it stops at various schools and had a break at St Christophe(?) for some other buses to link with us. Once in Rodez I went into the railway station- the bus stopped here- and found out that there was a bus soon leaving for Montauban. (There were trains also, but it was a much longer wait for one of those.) Once there I took the Toulouse bound train which stopped at Moissac.
The other option you have if it isn't a school day, is to take a taxi to St Christophe, where the Paris train passes. You catch a train in the other direction, but as I didn't take this option, I can't remember exactly where the train went to. The taxi to St Christophe wasn't very expensive.
There is 'pilgrim transport' out of Conques in the direction of Figeac or back to Le Puy in the season. I asked about this, but it never left Conques until around midday or later.
Margaret