- Shirley MacLaine wrote in her book "My Lucky Stars" that before filming on My Geisha (1962) began, Yves Montand bet Parker that he could seduce her. Parker, whom MacLaine learned later, was having an affair at the time, took Montand up on the bet; Montand won.
- Both he and then-wife Shirley MacLaine both had consenting permitted affairs frequently during their marriage.
- Father, with Shirley MacLaine, of Sachi Parker.
- Ex-brother-in-law of Warren Beatty.
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