The Bridget Jones's Diary star carried the little boy around as they made their way into the Louisiana restaurant. Zellweger rocked a casual look sporting a long-sleeved black jacket with a pair of dark khaki slacks. Anstead appeared cool in a white t-shirt and a pair of jeans.
The father-son duo have appeared to be having a ball during their visit to see the Texas native as she films the true crime drama The Thing About Pam. As OK! previously reported, Anstead took to Instagram earlier this week to rave about how much fun he was having traveling with his son.
"Getting on planes and seeing new things! He holds my hand the whole way and asks questions! He loves to hold his tickets and watch out the window," the proud dad wrote alongside pictures of Hudson during their airplane ride. "He loves to pack his own bag with his own snacks and he shares each of them with me (and whoever is sat near us 😂) ...We have way more travel planned……… ✈️ 🏃🏼♂️ x"
Anstead also made time to gush over his superstar girlfriend about how helpful she has been despite her hetic filming schedule.
"When your GF wakes up at 4am to get to work but still does the laundry and prepares a travel package to wake up to," the motor specialist wrote on his Instagram Story on November 30.
As OK! exclusively reported, the pair — who has been linked since June — may be thinking about taking the next step in their relationship.
“They’ve been talking about having a small ceremony in England soon, something elegant and tasteful," a source revealed. “They like the idea of an intimate dimly lit setting with candles, fresh flowers and a harpist. Renée wants them to write their own vows down and just say what’s in their hearts, and Ant’s all for that."