Under the two-part deal, Safran will launch a cash offer worth 29.47 euros per share, a 26 percent premium to Wednesday's Zodiac closing price of 23.31 euros.
The initial offer values Zodiac at just over 8.5 billion euros ($9 billion), based on Thomson Reuters data.
Zodiac shares jumped by 23 percent when trading opened in Paris in what could be their best performance in 30 years. Safran gained 0.7 percent.
Zodiac's controlling family shareholders would not take up this part of the offer, but would instead fold their shares into a subsequent merger between the two companies, based on 0.485 Safran shares for each Zodiac share.
In addition, Safran's existing shareholders would receive a special dividend of 5.5 euros per share, worth a total of 2.3 billion euros, before the deal goes ahead.
The companies said the combination would boost earnings per share from the first full financial year.
Zodiac Aerospace is controlled by a group of families that owns 23.8 percent of the stock and 36.6 percent of the voting rights and an arm of the Peugeot family, which owns 5.2 percent of the shares and holds 7.3 percent of the voting rights.
The French state owns 14 percent of Safran and will remain a shareholder of the combined group under a pact with other core shareholders.
Zodiac Aerospace is one of two major suppliers of aircraft seats alongside B/E Aerospace. The industry relies on demand for eye-catching interiors from airlines but has struggled to combine such one-off, customised projects with the factory pace and costs needed to keep up with a recent boom in jet orders.
Rockwell's acquisition of the latter, expected to be completed this spring, is designed to allow B/E to deploy Rockwell's capability with onboard connectivity to make internet-enabled seats and other cabin systems.
Other top suppliers seen as keen to expand include Honeywell , which failed to grab United Technologies in 2015.