What is the in-universe reason for Spock smiling in 'The Menagerie'?

The in-universe reason (from the original teleplay) is that he was "grinning with relief" at having discovered that the source of the strange noise was nothing more than an exotic plant.

16 EXT, TALOS XV RAVINE - LIMITED ANGLE DOWN

Revealing little or nothing but the ravine floor where we see a sudden eddy of dust as if the surface here is being blasted by an invisible force. Then, Winter and his landing party materialize, CAMERA IS EMPHASIZING Winter, allowing us to share his reaction at this first look at a strange new world. We HOLD an instant while Winter and the landing party look, registering some surprise, then:

17 ANOTHER ANGLE

Revealing the weird violet sky, twin suns, around them is multi-hued jagged rocks, here and there orangish vegetation not too dissimilar from Earth desert plants. Suddenly, a MUSICAL FLUTE-LIKE SOUND. The landing party reacts, then Mister Spock moves forward, grins in relief as he points out the source — a plant with paper-thin rigid leaves which vibrate in the breeze. He blows on it, produces new MUSICAL NOTES. (These wind-plant SOUNDS will identify and set mood for all our scenes on the surface of Talos IV).

We learn (in subsequent episodes of Trek) that Vulcans gain additional emotional control as they age. It creates a nice counterpoint to show a discernible difference in attitude between the younger/less experienced Spock, aged 24 years and pretty fresh from the Academy and the older Spock, aged 37 who's seen more than his fair share of death and destruction.