Paappi Appacha is the story of a father and son, Mathayi (Innocent) and Paappi (Dileep). They live like friends and they get into all sorts of mischief in their village, Ithirikkandam. Annie (Kavya Madhavan) works as a teacher in a local school and Paappi falls in love with her, though Annie does not like him. A businessman named Manikkunju comes to the village, which creates a lot of problems. Meanwhile Annie, with support from Shashankan Muthalali (Ashokan) and fellow school colleague Dasan maashe (Rajeev) stand against Paappi in election for panchayat president and wins.
Annie get a marriage proposal. Hearing this Paappi goes to Annie's house who sees him jumping to catch a glimpse of the proceedings. The would be groom tells he expects a positive response from Annie and leaves. Later she gets a call from the would be groom's mother who abuses her as her son was hit black and blue by Paappi. Annie, furious about this, goes to Mathayi's house and gives a piece of her mind and mathayi starts to doubt paappi. Paappi angry about this, acts rough to Annie during a school function and in a fit of rage accepts that he trashed her marriage proposal. Mathayi slaps paappi and a crack is formed in their relation. Things get bad when the school run by Mathayi's family is burned down and Mathayi completely disowns paappi thinking he is the culprit.
In the second half of the movie we can see Paappi trying to survive on his own along with trying to give Mathayi a hard time. Finally, Mathayi who is cunningly supported by Shashankan Muthalali falls for a trap set by paappi and is forced to sell Mariya's (KPAC Lalitha) land. But Paappi foils that plan also by making it appear that there was a treasure of old age items discovered from that plot, ending in the archaeological department taking over the land. The City market once run by Paappi and Mathayi together doesn't function the same anymore and Annie who had earlier taken a diary from paappi regarding the plans he had for the panchayat if he won the election, uses one ploy of panchayat buying the market items from farmers and selling it giving the profit to the farmers. She shares this idea with Dasan maashe who is also excited about this.
Mathayi and shashankan are walking on the roadside drunk. Both are attacked by Manikkunju and another person with sword. Mathayi is injured while shashankan escapes as the neighbors hear the commotion and comes out. Police try to catch paappi suspecting his hand but paappi escapes from their clutches. He also finds out that Annie is kidnapped. We see then Annie is captured by Manikkunju and in a struggle she tries to escape and finds Dasan maashe and asks for help. Manikkunju arrives and turns out that he is Dasan maashe's relative. Dasan maashe explains that Paappi and Mathayi are doing business on his land which was actually bought by Mathayi long time back when Dasan Maashe's, original name Sivadasa menon, father had to sell it to them due to his spendthrift ways. Dasan maashe tells annie that he likes her and even though he knows Annie loves Paappi, her body will belong to him and tries to rape her. But Paappi comes to the rescue and saves the day. Meanwhile mathayi also arrives learning the truth that it was Dasan maashe who disrupted annie's marriage proposal and also put fire in school building.