Payet was the star for hosts France, who won their opening game of the Euro 2016 finals 2-1 against Romania at Stade de France in Saint-Denis.
After a goalless first half, the home team took the lead on 57 minutes when Olivier Giroud turned in a delivery from the West Ham United attacking midfielder.
Bogdan Stancu pulled Romania level from the penalty spot o 65 minutes, but Payet made it 2-1 to the French with a stunning strike on 89 minutes.
The 2-1 win in their opening Group A game means that France have a great chance of progressing to the knockout stages.
Former Leicester City and Tottenham striker Lineker was following the match, and he was impressed with Payet.
The former Marseille star’s performance for France also impressed Crystal Palace chairman Steve Parish and ex-west Ham winger Trevor Sinclair.
Payet has been exceptional, as he has been all season for West Ham.— Gary Lineker (@GaryLineker) June 10, 2016
WOW. What a goal from the best player on the pitch. Monsieur Payet, well played!— Gary Lineker (@GaryLineker) June 10, 2016
Another level that's all I'm saying— Trevor Sinclair (@trevor8sinclair) June 10, 2016
Payet scored nine goals and created 116 chances in 30 Premier League appearances for West Ham during the 2015-16 season.