If you're looking for a meeting place or a good stop around ½ or halfway between Paris, TX and Plano, you can try Edhube, TX, which is almost an hour west of Paris, TX, or almost an hour northeast of Plano.
Another possible place to stop near the midpoint is Union Hill.
About ¼ or a fourth of the way, you can stop at Honey Grove, TX. This is about half an hour west of Paris, TX.
About ⅓ or a third of the way, you can stop at Lannius, TX. This is about half an hour west of Paris, TX.
About ⅔ or two thirds of the way, you can stop at Nobility, TX. This is about 1 hour southwest of Paris, TX, or about half an hour northeast of Plano.
About ¾ or three fourths of the way, you can stop at Melissa, TX. This is a little over 1 hour southwest of Paris, TX, or about half an hour north of Plano.
If you drive straight through without stopping at all, the total distance is 92 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 1 hour, 38 minutes.