Williams had to fight off a determined Hogenkamp in the first set but dominated throughout the second when her 108th-ranked opponent, who spent almost three hours on the court in Saturday's loss to CoCo Vandeweghe, showed little resistance.
Serena Williams played in a tennis tournament in front of her baby daughter Alexis for the first time this weekend.
"Honestly, I like to think that CoCo wore her (Hogenkamp) down some yesterday", said Williams, who then took to the court with younger sister Serena for a doubles dead rubber. "Or I'll get angry about the crying, then sad about being angry, and then guilty, like, 'Why do I feel so sad when I have a lovely baby?' The emotions are insane".
Serena Williams had said her return to tennis would represent the "start of a long process".
Serena was scheduled to compete in the Australian Open this January, but made a decision to pull out after losing an exhibition match in December. This is literally my first time traveling with the baby and everything.
"Serena's gonna be joining her sister Venus!" she announced, to roars of approval before the superstar appeared dressed in a white top, dark blue shorts topped off with a red headband.The sisters have won 22 doubles titles together, the last of which was Wimbledon in 2016.
Mladenovic double-faulted on her first match point at 40-15 but delivered a strong serve on the next point which proved enough, sparking wild celebrations from captain Yannick Noah and French staff members at the indoor court in La Roche Sur Yon in western. "I didn't manage my time well, but I was thinking about it, in the future, how to manage it better".
But shortly after, the owner on an Open-era record 23 grand slam singles titles drew wild cheers when she confidently stepped to the net and stretched out to drive home a superb backhand volley. "I'm always going to have the best and highest expectations for myself".