Minority shareholders had hoped to see Wendy Lane and Jesper Brandgaard, presented as experienced directors with knowledge of sensitive governance issues, join the board on Thursday.
But the resolution to appoint Lane was rejected with a majority of 56.2 percent, while the one to appoint Brandgaard was rejected with a majority of 65.74 percent.
The board had advised shareholders to reject the proposals ahead of the annual meeting on the grounds that new appointments would jeopardise the balance of the current board, which has an equal number of members from both sides.
"We are very disappointed. And I fear the disagreements could resurface," Denis Branche, managing director with asset manager Phitrust, an EssilorLuxottica shareholder, told Reuters.
Shares in Essilor, which have been under pressure in recent months, were up 0.88 percent at 1514 GMT.
French firm Essilor and Italy's Luxottica are supposed to have equal weight in the combined group's leadership until 2021, but the French and Italians have accused each other of trying to dominate the 54 billion euro ($60 billion) alliance.
The group's top executives, Italy's Leonardo Del Vecchio and France's Hubert Sagnieres, attempted to put tensions behind them on Thursday, saying the best was yet to come and touting bi-monthly meetings of working groups focused on the merger.
Integration teams have so far identified some 20 projects to help streamline the merger, ranging from research and development to retail and marketing.
"EssilorLuxottica continues to operate and to take important decisions. The first quarter results were outstanding," Sagnieres told reporters.
Earlier this month, the company posted higher first-quarter sales and maintained full-year targets.
CEO SEARCH CHALLENGING
EssilorLuxottica took the first steps to ease tensions on Monday with the appointment of two senior executives to speed up the merger and ensure 'synergies' are delivered on time. A new chief executive is to be hired by the end of 2020.
"EssilorLuxottica has perhaps not shown the best of itself, but this week's agreement marks a new beginning," said Laurent Vacherot, chief executive of Essilor, at Thursday's meeting.
However, Del Vecchio, Luxottica's founder and the largest shareholder in the new entity, described the search for a new CEO as "challenging", in another sign that the drama at the very top was not over yet.
Two headhunters are currently looking for candidates, although Del Vecchio said he favoured internal talent.
"We don't want a banker or a lawyer to pilot this complex group, that will not work," he said.
Tensions over the merger first arose in November 2018, a month after the deal was finalised, when Del Vecchio appeared to tap his right-hand man, Luxottica chief executive Francesco Milleri, as the next group CEO.
Although Milleri and Vacherot have been given more powers this week, they both said they would not run for the top job.
(Reporting by Matthias Blamont. Additional reporting by Claudia Cristoferi in Milan; Editing by Sudip Kar-Gupta and Alexandra Hudson)
By Matthias Blamont