A video emerged online of the Hoops captain being asked "How's your sister?" by a Rangers fan as he made his way out of the stadium after his side's 2-0 win.
Brown's younger sister, Fiona, died in 2008 following a battle with skin cancer.
• READ MORE - Boy, 15, charged after Celtic captain Scott Brown taunted over sister outside Rangers stadium following Old Firm clashPolice Scotland say a 15-year-old male has been "charged and referred to the Early and Effective Intervention Co-ordinator" while Rangers say he has been banned for life.
Jullien has said: "I didn't see the video, but I've heard about it. I don't think it's good behaviour. It's not welcome in every stadium.
"We are with Broony. We are giving Broony all the support he needs but I don't know what else to say. It's just ugly. I don't like that."