Did Bail Organa tell his wife about Leia's parentage?

Question

Bail Organa mentioned how his wife had always wanted to adopt a baby girl. It was also imperative that the Skywalker twins were to be kept as far away from the Sith as possible, with their existence and identities kept secret. Given how the Sith operate, it would be prudent to have as few people know the truth as possible.

Therefore, there was good reason for Bail Organa to just bring Leia to his wife and go "Hey honey look, I just adopted a baby girl just like you always wanted!" without ever mentioning how she's the daughter of Anakin Skywalker and Padme Amidala - highly scandalous and controversial news considering recent events.

But did he? Did Bail Organa tell his wife nothing about Leia's parentage?

Answer 1

Unclear, probably not

According to Bail's page on the Star Wars Encylcopedia (the precursor to the Databank), the answer would seem to be "no":

Bail Organa and the Queen of Alderaan adopted Leia as a newborn. Only Bail, Obi-Wan Kenobi and Yoda knew that young Leia was the offspring of Anakin Skywalker and Padmé Amidala.

However, since the Encyclopedia was subsumed by the Databank shortly after Disney's canon re-organization¹, and this information doesn't appear on any of Bail's, Leia's, or Breha's databank pages, it's not clear that this information is still canon. Unfortunately, it's about the best we can do at this point; as far as I know, this question isn't answered by any more recent materials.

That being said, I find it unlikely that he would tell her; the more people who know that either Anakin or Padmé had children, the more likely it is that word would eventually reach Vader and/or the Emperor, which would rather undermine the point of hiding them.

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¹ The Wayback Machine's last archive of Bail's page is in January 2014, but the Encyclopedia itself continued to exist until the end of June, after the official (April 2014) announcement of the new canon stratification

Answer 2

Breha Organa didn't know about Leia's parentage. When Bail was still alive he left a confidential recording with his political ally, the supreme governor of Birren. The message was for Leia's ears only and to be delivered to her in the event of his death. Bail didn't take into account that she may have heard the info from any other source (e.g. his wife) other than himself

“My beloved daughter,” he said. “The supreme governor of Birren, whom I trust completely, said that he would keep this here for you when you someday inherit this title. My hope is that this recording contains no new information, that I have had the chance to explain everything to you myself.”

“Obi-Wan Kenobi took your brother for safekeeping, and I took you. We hid you both from each other, and from your father, who could not know that any child of his had been born alive. You see, Leia, I always told you the truth about your mother and how she died. But I never told you that she was Padmé Amidala, former queen and senator of the planet Naboo.”

“Nor could I share that your father was Anakin Skywalker, one of the last Jedi Knights and a great hero of the Clone Wars. But now I must tell you the worst, and you must be strong. I must tell you what became of Anakin Skywalker.”

“Your father has become Darth Vader.”

_{^{Star Wars: Bloodline}}

Critically, he describes this info as

knowledge you—and only you—have the right to possess.

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It would appear that Bail's wife knew the same that the public knew, that Leia was an orphan of the Clone War. She evidently didn't know that she was the daughter of Padmé, nor that Anakin Skywalker was her father or that Anakin had become Vader.