Paris to Madrid by train

The only option for making a journey by train in a single day by train from Paris to Madrid involves departing the French capital at 10:14 (departure times can be altered on certain dates).

The TGV from Paris is typically scheduled to arrive in Barcelona at 16:54, but the end-to-end journey time of 10hr 1min and an arrival into Madrid at 20:15 is dependent on taking a more-basic, but still high speed Ouigo service and not a regular AVE train.
if you want to travel in the equivalents of 2nd class worth comparing the two services on the 'Trains Guides', but there is no equivalent of 1st class available on a Ouigo service

The Ouigo service will be typically scheduled to depart from Barcelona at 17:40 and the AVE service is scheduled to depart at 18:25, but not on Saturdays, when the first AVE departure after the arrival from Paris, wont be typically available until 19:00

When SMTJ was last at Barcelona Sants there were staff on the platform holding up signs for Madrid, so they could be approached by passengers who would then assist with the onward transfer.

Book early and save: Yes

Online bookings usually open: 4 months ahead of the travel date

It's worth comparing prices across these agents when looking up this journey, though keep in mind that both RailEurope and Trainline will charge a booking fee on this route.

In the event of a missed connection:

The train operating companies on this route have signed up to the AJC; the relatively new ‘Agreement for Journey Continuation’ policy, which has also been introduced to protect travellers using international railway tickets.

In effect the AJC stipulates that no matter what type of ticket you have booked, or have been issued with, you can continue your DAYTIME journey by a different train to that specified on your ticket, in the event of a delay to a preceding train.

Meaning that the AJC can also offer protection if you are using separate tickets per train, which you purchased by making multiple bookings.
However, Ouigo services are not included within this AJC agreement, so if you book the end-to-end journey which involves taking the Ouigo service on from Barcelona and a delay to the train from Paris causes a missed connection, you will have to re-book tickets for the 20:45 departure.
In contrast, if you book tickets for the end-to-end journey by a combination of TGV + AVE trains, you can transfer tickets at no cost to the AVE departures at 19:00; 19:25 or 20:00.