From Paris to Orléans, take a train at Austerlitz railway station.
There are two stations at Orléans. The first one is called "Les Aubrais" and the second one is called "Orléans". The best for you is to get off at "Orléans". But, if all trains stop at "Les Aubrais", not all of them go to "Orléans". So, you should try to buy a ticket for a train which goes to "Orléans". If not possible for you, get off at "Les Aubrais" and take the tram A in direction "Hôpital - La Source" and then get off at "Charles de Gaulle" stop.
The trains run quite often. You should check on this website:
Most of the trains (Intercités) are direct and take a bit more than one hour. Some other trains (TER) are longer (about one hour and forty minutes) because they have many stops between Paris and Orléans. Try to avoid them.