That honour went to Airbus which flew its new A350 jumbo jet for the first time on Friday.
Expectations had been high the CSeries would beat its rival to the punch. But the CSeries isn't slated to fly before the end of the month.
Spokeswoman Haley Dunne said Bombardier still expects its new 110- to 160-seat aircraft to generate a lot of interest at the air show.
"Headlines are great, and we've let everyone know that when we have our first flight that's going to be a great moment," she said from Paris.
"But we would never accelerate anything just to try and have it happen during this week of the year."
That also applies to orders.
Dunne described the show as a good opportunity to meet people, including suppliers, potential customers, governments and media. And if a deal is finalized, it will be announced.
"I don't think it's agreements that we wouldn't otherwise get," she said, adding that notching up orders isn't a signal of an air show's success.
"Success is building and maintaining good relationships with our stakeholders."
What Bombardier will announce at the show isn't clear. Though time has been set aside in the first three days for potential announcements, nothing has yet been finalized, Dunne said.
On Friday, the company issued a market forecast that pointed to a slight increase in the value of commercial and business aircraft orders over the next 20 years, but it didn`t change the outlook for the number of planes it expects to sell.
Boeing and Airbus are expected to announce hundreds of new orders for their aircraft in Paris. At last year's event in Farnborough, outside of London, the two companies accounted for 75 per cent of the US$72 billion worth of orders placed for 758 aircraft.
To date Bombardier has received orders and commitment for a total of 388 aircraft from 13 customers, including 177 firm orders.
More than 100 Bombardier officials, including most of the company's senior aerospace executives, will participate in the five-day Paris trade show that features commercial and defence aircraft.
There's been talk among analysts that Bombardier might announce some plane orders at the show, with speculation centring on possible deals with EasyJet, Swiss Air and a Chinese carrier.
Walter Spracklin of RBC Capital Markets is bullish on Bombardier orders.
"With still more regional orders expected in 2013, the Paris Air Show and the CSeries first flight in June, there is an increasing probability that Bombardier is on the cusp of a new CSeries order cycle," he wrote in a report.
He said Bombardier's market forecast signals continued faith that the CSeries will generate strong revenues. The manufacturer expects to make $138 billion to $230 billion in revenue over two decades with a $3.4 billion development program.
"Even with more pessimistic margin assumptions ... the CSeries program will no doubt be viewed as a financial success, in our opinion," Spracklin wrote.
David Tyerman of Canaccord Genuity said the prospects of Bombardier landing more CSeries orders is good, though he doesn't have high expectations they will necessarily come at the Paris air show.
Nor does he feel the company missed a golden opportunity with the plane's first flight coming after the air show.
"At the end of the day, the show is a time for people to be able to go and kick the tires and so on. If the plane is in the air or not at this point or two weeks later is probably pretty irrelevant to most of the clients," he said from Paris.
Tyerman added that Bombardier's focus after first flight will be to get more orders, complete certification and try to stick with plans for entry into service in June of next year.
The analyst said history has shown that these air shows don't really affect the company's share price.
"This show has proven in the last six years to be a bit of a non-event from a stock standpoint for Bombardier. I suspect it probably will be again this year."