Bedene fell a set down to the Frenchman before fighting back to reach the last 16.
Chardy, the eighth seed in Valencia, broke straight away to go 2-0 in front and then broke for a second time four games later after Bedene had briefly restored parity.
Chardy closed out the set with ease and then held his first two service games at the start of the second to move 2-1 ahead.
Bedene then roared back by winning five of the next six games to claim the set 6-2.
The momentum was with the world number 48 and although he missed out on three break points in the first game of the third, he had soon broken again and wrapped up the match 6-1 as Chardy fell away.
Up next for Bedene in round two is a match against Canada's Vasek Pospisil.