If you have an eticket, then they should find it in their system. By booking number make sure your using the Air Transat number, flight no and last name or they can pull it up by ticket number.
Has your flight changed? Make sure it’s still shows operating on the Air Transat website.
Their website shows Eco and Club fares. They should be able to tell you what the rules are for seat selection.
Are you sure it is a Air Tranat flight and not operated by a code share? It will state so on their website.
I would check everything, flight number etc and then call the airline back. They should be able to figure it out, if you’re already ticketed.