If you're looking for a meeting place or a good stop around ½ or halfway between Paris, TX and Dallas, you can try Greenville, TX, which is almost an hour southwest of Paris, TX, or almost an hour northeast of Dallas.
Another possible place to stop near the midpoint is Campbell.
About ¼ or a fourth of the way, you can stop at Commerce, TX. This is about half an hour southwest of Paris, TX.
About ⅔ or two thirds of the way, you can stop at Hendrix, TX. This is about 1 hour southwest of Paris, TX, or about half an hour northeast of Dallas.
About ¾ or three fourths of the way, you can stop at Rockwall, TX. This is a little over 1 hour southwest of Paris, TX, or about half an hour northeast of Dallas.
If you drive straight through without stopping at all, the total distance is 104 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, 43 minutes.