Is it required or recommended to make reservations for this trip, or can I get tickets on the day when we arrive at the airport?
Check with the Man in Seat 61. It also matters if you're using a pass of some kind.
I do not have a pass. Who is the man in seat 61?
It is not required, but highly recommended to have reservations, however you can get tickets on the day if there is capacity.
Booking ahead should also get you lower fares than on the day, as SNCF fares are dynamic- demand driven.
Looking on SNCF connect at 10pm UK time for tomorrow there is capacity on the 4 morning trains but both afternoon trains are 'complet' [full], then the 2 evening services currently have space, at a price
And on Wednesday all services after 12 noon are already full. On Thursday all departures after 12 noon are also full. On Friday all services from CDG between 0945 and 1819 are full.
So you have to take a best guess on whether you will land late, and how long it will take to get through the airport.
The alternative is to take the RER into Paris as there are more departures from Montparnasse station, but even there many of the departures tomorrow afternoon are already 'complet' so that is no guarantee of success either.
When is the trip?
You can get tickets on that route the same day.
However sometimes the train sells out, like during peak tourists travels season June July August.
If you buy the ticket in advance it is cheaper but you should select a flexible refundable ticket since it is never guaranteed that your flight is going to arrive on time for you to catch the train.
Mark Smith is a former rail industry exec (according to Wikipedia) whose website has become an essential train travel tool (according to his many fans.) The nickname apparently identifies his favourite First Class seat on the Eurostar service between Britain and the continent.