"relaxed smile" is correct and usable in written English.
You can use it to describe the kind of smile someone is displaying. For example, "He greeted her with a relaxed smile".
Since 1999, Mr Biskup has also photographed Mrs Merkel around twice a year, producing near-faultless portraits of a relaxed, smiling Chancellor.
William spent more than six hours with his wife in hospital yesterday and left at 5.45pm looking relaxed, smiling at the waiting reporters and photographers.
Thomas, 46, in a gray suit, looked relaxed, smiling occasionally, and at breaks in the questioning of the jurors, laughed with his three lawyers, all of them women.
The other first-year class had only 28, and they visibly relaxed, smiling, when I appeared, my pile of marked exercise books carried proudly by a keen lad with a shining face whose given name was Slumber.
Before Monday morning's hearing, Mr. Martoma and his wife, who have three young children, appeared relaxed, smiling and chatting over breakfast in the courthouse cafeteria with Mr. Stillman and his law partner, James A. Mitchell.
He relaxed, smiling as he looked out the window at the low empty hills, the creases of green in the landscape which marked the foliage along rivers and creeks, the villages made visible by the smoke rising from cooking fires.
Sitting in the office of his criminal lawyer last month, relaxed, smiling and dressed in a crisp blue suit and red-and-blue tie, Mr. Lavrentiadis said he found it puzzling that he had been singled out in reports about the Lagarde list when other powerful figures appeared to evade scrutiny.
He appeared relaxed, smiling at what appeared to be family members in the courtroom.
