I have purchased a Eurail pass for one country, France. Can I purchase tickets on the spot on the day of travel? And is there any cost if I do it at the station?
When you travel on a Eurail pass you do not need to buy tickets.
You may need reservations and pay surcharges and you will get something that looks like a ticket as used in that area, but it is not a ticket. On the other hand, if you travel on the local trains, you do not need a ticket at all.
If you have a one country pass it is likely that you are restricted in the number of days you can use it. You can buy tickets for those days you do not want to spend a day on the pass, but in that case it is like you do not have a pass at all. You can buy the tickets ahead of time online or at the station or on the day itself, also online and at the station.
Buying tickets for longer distances or the fast trains and buying reservations and if needed surcharges for those same trains does not differ much.
For many travels you can wait till the last day, the last few minutes, but you are not sure of a reservation or ticket. If you know you want to travel for sure on that day and time, buy the ticket or get the reservation as soon as you can.
There are a few trains for which there are limited amount of reservations for travels on a pass. For those trains you need to make your reservations early or be prepared to use trains that are less popular, likely with a connection or at a less wanted time of the day. I am not sure whether there are 'within France' trains with that restriction, but I do know that the Thalys trains, (Paris to Brussels/Amsterdam) have the restrictions and likely other internatonal trains as well.
(I am not connected with Seat 61 at all, just a happy user of the site.)