The 24-year-old Berdych, who won in Paris in 2005, served 10 aces and broke his opponent three times on his way to his one hour and 25 minutes victory.
The 247th-ranked Millot wasted a 5-2 lead in the second set and his Czech opponent finished the match with an ace on his first match point.
Berdych, a former world No. 9 who is currently 20th in the ATP rankings, will next face 14th-seeded Tommy Robredo of Spain.
Italian Andreas Seppi beat Philipp Kohlschreiber of Germany 6-3, 6-3 after winning nearly 75 percent of the points played on his serve while Ivo Karlovic of Croatia served 21 aces and reached the second round with a 7-6 (3), 6-4 victory over Pablo Cuevas of Uruguay.
Former three-time champion Marat Safin of Russia, who is planning to retire after this tournament, will take on French qualifier Thierry Ascione later Monday.
Another former winner, Sebastien Grosjean of France, will face 2005 runner-up Ivan Ljubicic of Croatia in the final match of the evening.
Seven players can still qualify for this month's eight-man ATP World Tour Finals in London. No. 7 Nikolay Davydenko and No. 8 Fernando Verdasco, a semi-finalist last week in Valencia, are in the best position ahead of Robin Soderling, Fernando Gonzalez, Jo-Wilfried Tsonga, Radek Stepanek and Marin Cilic.