In a letter to shareholders, Fontaine called for the replacement of two directors and said Bounty should not have sold its stakes in two offshore northern Perth Basin permits to Arc Energy.
He now wants to develop key projects for Bounty but does not believe the current board will see such projects favourably or be able to implement them.
However, managing director Laurence Roe has countered Fontaine's move to change the board with a call to remove Fontaine from his directorship.
Bounty said it would also pursue legal action against Fontaine in order to have him reimburse US$22,800 paid in relation to work he undertook at the Nyuni prospect in Tanzania.
Fontaine has said he was unconcerned about any possible legal action and was more interested in changing the direction of the company.
In August, Bounty sold its 7.5% interests in WA-325-P and WA-327-P for A$1 million cash.
An additional amount of up to A$2 million will be payable to Bounty on certain success thresholds being met following the drilling of the next two exploration wells in those permits. The thresholds are based on a subsequent start of appraisal drilling, the declaration of commerciality and the beginning of production.
Bounty managing director Laurence Roe said this deal allowed Bounty to further focus on its producing assets.
But Fontaine said the stakes should not have been sold.
The Hadda-1 well drilled in WA-325-P in March was unsuccessful, but its oil shows in tight sands pointed to the possibility of a new exploration fairway in that area, Fontaine said. The Blue Jacket prospect is also in that permit, while WA-327-P contains the Flying Foam prospect.
The permits were also adjacent to the cliff head oil development, he said.
Fontaine argued that Bounty should have pursued alternative funding arrangments through a share placement.
Fontaine founded Bounty and is a former managing director. He is still a major shareholder.
He is also managing director of White Sands Petroleum, a company in which Bounty has a 25% stake.