Murray, who reached the semi-finals of last week's French Open, had been handed a bye in the first round of the grass tournament.
A winner at Queen's three times previously, including last year, the British number one put in a workmanlike performance on Wednesday afternoon, taking victory over his French opponent 6-4, 6-4 in one hour 26 minutes.
It extends his winning run on grass to 19 matches, stretching back to his Wimbledon final defeat to Roger Federer in 2012.
The result also marked a winning start to his partnership with new coach Amelie Mauresmo after they announced they were to work together for the grass-court season.
"It was a good start; I served pretty well," said Murray, who will now face Radek Stepanek in the last eight on Thursday.
"Both of us moved well, there were some good rallies and it was a good start to the grass-court season."
Queen's singles round two results
3-Andy Murray (Britain) beat Paul-Henri Mathieu (France) 6-4 6-4
Kenny De Schepper (France) beat 6-Ernests Gulbis (Latvia) 7-6(3) 7-5
8-Alexandr Dolgopolov (Ukraine) beat Denis Istomin (Uzbekistan) 7-6(3) 7-6(7)
Sergiy Stakhovsky (Ukraine) beat 11-Vasek Pospisil (Canada) 6-4 6-4
Jarkko Nieminen (Finland) beat 12-Dmitry Tursunov (Russia) 7-6(3) 7-6(3)
Edouard Roger-Vasselin (France) beat 13-Nicolas Mahut (France) 6-3 1-6 7-6(5)
15-Radek Stepanek (Czech Republic) beat Bernard Tomic (Australia) 7-6(4) 7-6(5)
Adrian Mannarino (France) beat Victor Estrella (Dominican Republic) 6-1 6-2
Marinko Matosevic (Australia) beat Lukas Lacko (Slovakia) 7-6(3) 6-3
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