"I am hopeful that the United States will give us permission to deliver these ATRs," Le Maire told French broadcaster BFM TV.
"There were eight to be delivered before August 6," he added, highlighting the "significant share" of the order for ATR’s turnover.
Deliveries of turboprop aircraft were halted in May after the withdrawal of the United States - which must approve any export of aircraft containing more than 10% US-made components - from the Iran nuclear deal and the return of the US sanctions regime against the Islamic Republic.
The equally-owned group by Airbus and the Italian Leonardo had warned earlier this month of the "serious implication" of the decision.
Le Maire expressed his optimism for other sectors, without going into detail.
"I've been negotiating for weeks with my counterpart, US Treasury Secretary Steven Mnuchin, and I'm hopeful we'll get on a number of topics that directly affect our SMEs (small and medium-sized enterprises) and our jobs in US-owned territories," he said.
"I am also fighting so that in the health sector, in the agri-food sector, which are now out of sanction, there may be funding channels that remain open," said the French minister.
France had sought, along with other European countries, exemptions from US sanctions for its companies trading with Iran, a request to which the United States objected.
A top US official made it clear last month that the US government was unlikely to approve a new request by ATR to sell more turboprops to Iranian carriers.
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he official likewise said the US government was unlikely to issue any licenses that would allow companies like Airbus and ATR to continue supporting aircraft in service with Iranian airlines.
ATR Chief Executive Christian Scherer warned last month of “serious damage” to ATR's finances from the breakdown of deals to sell 20 planes to national flag carrier IranAir, eight of which have been delivered so far.
Iran received the first four ATR aircraft last May, two more in September, beside another two in December, with the rest due to be handed over to the country by the end of 2018.
The first group of sanctions on Iran’s automotive sector, gold trade, and other industries will “snap back” on August 6. Further sanctions on oil and transactions with the central bank of Iran will come into effect November 4.