Two sets to one up overnight, the 13th seed wrapped up a deserved victory with some scintillating shots to deflate an expectant Centre Court crowd.
Henman, seeded 10, had been hoping to reach his fifth Wimbledon semi-final in six years but the host nation's hopes of a first men's champion since 1936 were left in tatters by some sublime shot-making from Grosjean.
The Frenchman will play his first Wimbledon semi-final against either German Alexander Popp or Australian Mark Philippoussis, who like Popp is unseeded.
Grosjean is only the third player from France to reach the semi-finals of the men's singles at Wimbledon since the game turned professional in 1968.
RODDICK TOOD GOOD FOR BJORKMAN
Andy Roddick made up for a day-and-a-half spent watching a variety of Wimbledon rainfall to storm past Swede Jonas Bjorkman 6-4, 6-2, 6-4 and also book his place in the men's singles semi-final.
Any hope Bjorkman had that Wednesday's downpours and Thursday's drizzle would have dampened fifth-seed Roddick's gunpowder were removed as the 20-year-old American blasted down serves of 128, 133, 132 and 125 miles per hour in his first service game.
That set the tone of a match between the youngest and oldest men left in the draw as Bjorkman found the pace too hot.
The 31-year-old did manage to break once in the first set but there was an air of inevitability as Roddick powered through the opener in 32 minutes.
Roddick, who had lost his only previous meeting with Bjorkman, dominated completely in the second set with booming serves and fizzing returns to leave the Swede dispirited.
There was no way back for Bjorkman as Roddick broke in the seventh game of the third set before clinching a 10th consecutive win in one hour and 32 minutes.