Elliott also wants Pernod to improve corporate governance and has suggested 500 million euros in cost cuts and options such as merging with another spirits company.
Elliott declined to comment.
Pernod said between now and 2021 it plans to raise its operating profit margin by 50-60 basis points per year, provided it can deliver annual organic sales growth of 4-7 percent, having achieved 6 percent growth in the 2017/18 year.
It also announced plans to make 100 million euros ($113.6 million) in cost savings to drive this margin expansion.
Pernod shares were up 1.7 percent by 0905 GMT.
Last month Pernod Ricard took a step towards improving its governance, naming Patricia Barbizet to the newly created role of lead independent director.
CEO Ricard, the 46-year-old grandson of the firm's founder, made sales growth his top priority when he took over in 2015.
He has defended his long-term value strategy which - helped by a recovery in Chinese demand for premium spirits - saw sales growth rise to 6 percent in 2017/18 and 7.8 percent in the first-half of 2018/19.
The company has been working since the summer of 2018 on a new three-year strategy plan dubbed "Transform and Accelerate".
It said on Thursday it expected to deliver a promised 200 million euros in savings by June 2019, a year ahead of their initial target.
However, analysts have said more could be done at Pernod Ricard, which had a profit margin of 26.23 percent in 2017/18 against rival Diageo's 31.4 percent.
First-half organic current operating profit advanced 12.8 percent to 1.654 billion euros on group sales up 7.8 percent to 5.185 billion, buoyed by a 28 percent jump in China sales.
Pernod's robust first half benefited from advance shipments of cognac in China ahead of the Mid-Autumn Festival and Chinese New Year.
Pernod reiterated that it expected second-half sales growth to moderate notably for Martell cognac in China but Ricard told Reuters he remained confident on China.