The 6-4 6-3 loss marked the first time Erakovic, 21, has failed to make to the second round in five appearances in the WTA Tour event in Auckland.
The result also ended New Zealand participation in the tournament, with Erakovic and Slovenian partner Polona Hercog losing in their first-round doubles yesterday.
World No 49 Cornet, 19, produced some solid, accurate ground strokes as she wrapped up the win over her wildcard opponent in one hour and 24 minutes.
Erakovic, whose ranking has dropped to 227 after an injury-plagued 2009, had her moments.
But she struggled with her serving in the opening set and appeared to be still working her way back to full match sharpness after being sidelined from March to October.