The 35-year-old - who competed for Harris's affections on the fifth season of the ABC show - was discovered dead along a remote area off a highway in Riverside, CA on Wednesday.
Writing on her Twitter account, Harris said: "Please say a prayer for the loss of a friend this morning. Life is fragile, don't forget to love the ones you love."
According to the Vancouver Sun, the Canadian-born interior designer later issued a statement saying that her heart went out to Hug's family.
"It's very difficult to find the words to express my condolences," she added. "But I will always remember Julien's gentle demeanor and kind heart, which will be sadly missed."
Fellow Bachelorette contestant Kiptyn Locke has also expressed his condolences on Twitter, writing: "Sad news last night of a lost friend. A reminder to appreciate every day & tell those around u they are loved. Today I'm celebrating life (sic)."
Hug's cause of death has yet to be revealed.