Janaka was not ploughing for farming purposes, he was doing the ceremonial ploughing performed in the beginning of a Yagna, as described in this chapter of the Bala Kanda of the Ramayana:
Later, when I was ploughing the ritual field then raised by the plough [from the furrow is a baby girl... since she is] gained while consecrating the ritual-field, she is named as Seetha, and thus she is renowned. Hers is a non-uterine birth as she surfaced from the surface of the earth, but fostered as my own soul-born girl and I determined [to give her in marriage to a bridegroom where his] boldness is the only bounty.
By the way, this is the same way that Venkateshwara's wife Padmavathi was born; the king Akasa Raja was doing the ceremonial ploughing for a Putrakameshthi Yagna when he spotted a baby girl. See the Tirumala Sthala Purana I linked to in my question herehere.