Unions representing workers at the French company were openly hostile to the appointment of Smith, chief operating officer at Air Canada, accusing the group of handing control to a foreigner and not protecting Air France's interests.
Air France-KLM shares fell 4 percent and were among the worst-performing stocks on Paris' SBF-120 <.SBF120> index.
"Driving the share price is essentially the discontent of the unions," Meriem Mokdad, fund manager at Paris-based Roche-Brune Asset Management, said.
Smith, who will take up his post before the end of September, will have to deal with labour troubles at Air France that have already cost the airline 335 million euros (£300.3 million) this year, forced the resignation of his predecessor, and seen the group's shares slump 36 percent in 2018.
French unions are due to discuss another round of strike action on Aug. 27.
Meanwhile, in the Netherlands, the Dutch pilots union VNV said it would strike unless the airline's management comes up with improved offers to ease their workload.
The union said work stoppages could begin in four weeks time, after it rejected a last minute offer made by KLM late on Thursday.
The union wants the Dutch arm of Air France-KLM to start hiring new flight personnel as soon as possible, to give pilots more time in between flights. KLM said it is already recruiting new staff, but that it is impossible to meet all the union's demands.
Air France took over KLM in 2003 when the Dutch airline was struggling, but the two have continued to operate independently.
Air France-KLM in May said it expected profits to fall this year due to the effect of strikes at its French business.
The French government has a stake of about 14 percent in Air France-KLM, while Delta Airlines and China Eastern Airlines each hold 8.8 percent.
In a research note titled "New CEO - New solutions to old problems", Societe Generale welcomed Smith's appointment but maintained its "sell" recommendation on Air France-KLM shares.
"(Smith) played a key role in Air Canada's (AC) growth and modernisation strategy in recent years, redefined AC's hub strategy and was also a driving force behind AC's successful low-cost brand Rouge," SocGen wrote.
SocGen noted that Smith's predecessor, Jean-Marc Janaillac, met stiff union resistance when he began the job. In the end, Janaillac lasted two years before quitting after Air France staff rejected his final salary increase offer.
"We hope that history won't repeat itself – otherwise having a non-French CEO will be the least of the group's and the (French) employees' worries," SocGen wrote.
KLM has had more success in cutting costs than its French counterpart. The Dutch airline managed to agree several cost cutting deals with its staff in recent years, which improved its profitability and put it in a stronger position than French partner Air France.
"Our pilots have given up a lot in recent years, making KLM profitable", VNV spokesman Joost van Doesburg said. "Now it's time for KLM to deal with its exhausted staff."
(Reporting by Sudip Kar-Gupta in Paris and Bart Meijer in Amsterdam; editing by Richard Lough and Jane Merriman)
By Bart H. Meijer and Sudip Kar-Gupta