Maybe there are regional differences, but I would not say "I am going to see with (Julie), but etc etc" as it is used in the sentence in this exercise. That would be "I am going to check with Julie, but . . . " or "I am going to see what Julie says/thinks, but. . . .".
It reads to me as if the literal translation from the French expression "Je vais voir avec Julie, mais ..." has been used here, but it doesn't sound right (to me) in English.
"I am going to see with Julie, but . . " would indicate something along the lines of 'keeping an eye on her', 'giving her a chance to' etc
