The former Arsenal man replaced Tim Sherwood at Villa back in November, as the club seeks to avoid another relegation battle this season.
He is yet to taste victory as manager, with two draws and two defeats taken in since he took charge at Villa Park.
They are currently bottom of the table with just six points, and seven adrift of safety, but Wenger believes Garde has the competency and intelligence to change things.
“I spoke with him before he took the job, now I let him work,” he told arsenal.com.
“But he has the competence and intelligence. He has a good team around him, he is at a big club, so I let him work.”
If Garde is to save Villa from relegation, it will be pivotal for him to get his French contingent to start performing.
Sherwood brought in a number of signings from Ligue 1 in the summer, but the likes of Idrissa Gueye, Jordan Veretout, Jordan Ayew and Jordan Amavi have all failed to impress so far.
There are hopes that Garde can change that, though, with him able to break through the language barrier that is sure to have been a problem up until now.
Whether that starts with a win over Arsenal this weekend, remains to be seen.