The “blank forms” are actually lettres de cachet singed by the king to send anyone who has them to prison by writing in the prisoner’s name.
The blank forms were not literally blank. This refers to the papers that were signed to send Dr. Manette to prison. In other words, since the Monsieur St. Evremonde had the standing and money to get his hands on the forms, he had “the privilege of filling up blank forms for the consignment of any one to the oblivion of a prison for any length of time.” (Book 1, ch 5, pg. 17 of the enotes etext)
Dr. Manette did nothing wrong. One of the reasons he is able to be released from prison, but also a reason he will need to be “recalled to life” since innocent men do sometimes have a harder time in prison.
The abuses of lettres de cachet by the French nobility was a cause of the French Revolution.
The "blank forms" mentioned by Mr. Lorry in Book the First, Chapter 4 of A Tale of Two Cities are the French lettres de cachet (French for "hidden letters"). These are letters that are signed by the king and countersigned by a secretary of state. They were employed to authorize the imprisonment of an individual. Under the ancien régime in France these were abused by the aristocracy to authorize someone's imprisonment.
Later in the narrative, the reason for the imprisonment of Dr. Manette is revealed. But at this point in the novel, Mr. Lorry simply mentions to Miss Lucie Manette these letters in reference to Dr. Manette, her father. He tells her that these "blank forms" were filled out in order to consign her father to the "oblivion of prison." Further, he explains to Lucie that her mother led her to believe that Dr. Manette died so that her daughter would not be anxious about him. However, Mr. Lorry explains, her father is actually alive. "Greatly changed, it is too probable; almost a wreck, it is possible...." Mr. Lorry also tells Lucie. He explains that her father has been in prison under a different name and for a long time, so he may be greatly changed.