What does "franchise-low debut weekend haul" mean?
"Franchise-low debut weekend haul" means, as P. E. Dant said, "the lowest amount a film that's part of the Transformers franchise has earned on its first weekend."
A series of related films (e.g., Star Wars, Transformers, Hunger Games) are often referred to as a franchise.
The first weekend a movie is open in theaters is its debut weekend. Earnings numbers for movies often refer to their weekend earnings because that's when the most people are off work and free to see movies, so weekend numbers typically dwarf weekday numbers. It's not a good comparison to compare the opening-day earnings of a movie that comes out on a Tuesday to a movie that comes out on a Saturday, so film studios look at the debut weekend numbers to get a truer comparison.
And haul here is being used as a noun to mean, as dictionary.com puts it, "something taken or acquired." Usually you'd reserve the word "haul" for reference to something especially valuable. So if a group of thieves robbed the cash register at a hamburger place, probably you wouldn't call the money they made away with a haul. But if they stole a bunch of diamonds from a jewelry store, then you could call the diamonds their haul. In the case, even though the film's earnings weren't very good compared to other films in the series, the movie still earned tens of millions of dollars in under a week, so that's definitely a haul.
Do you have to pay for previews?
Yes, I believe user3169 nailed this one saying that "Tuesday night previews" here refers to paid showings on Tuesday night. Presumably, the film officially opened on Wednesday. Not just anyone is necessarily able to buy tickets to the early preview showings, but those that can get them would still have to pay.
That can be a bit confusing because, as it relates to movies, you also have another meaning for "previews" that refers to the trailers for upcoming movies you see in the theaters before the actual movie you're there to watch starts. For those, the audience doesn't pay to see them, and the movies doing the advertising are paying the theater to show their previews.