If the deal leads to a loss of value for Safran "we would have no choice but to seek to recover the damage suffered by the company from you personally", the activist fund said in a letter seen by the Financial Times.
This follows a letter from TCI to Safran last month which expressed "strong opposition to the takeover of Zodiac Aerospace and [demanded] that Safran shareholders are given a vote on the merger before Safran proceeds with the takeover".
Safran is "significantly overpaying for Zodiac", TCI said, and shareholders "will suffer massive value destruction".
"We demand therefore that the board give Safran shareholders a vote on the merger before Safran initiates the tender offer for Zodiac," it said. Plans to hold a vote after a successful tender offer are "a cynical and outrageous attempt to force Safran shareholders to vote for a merger they may not really want", it said.
Zodiac Aerospace issued a profit warning this month, but said that "current headwinds and remaining industrial issues in seats UK and cabin do not affect our ambition to return to historical profitability by financial year 2019/2020".
Safran said that it had reviewed this information, and was still interested in the acquisition.
"Safran confirms its confidence in its own ability to restore the operating profitability of the businesses currently in difficulty," it said.