The question needs to be asked whether there have to be consequences (for management), Johannes Witt, a board member representing the interests of labour, told German weekly Euro am Sonntag in comments published on Saturday.
Can someone who wanted to change the status quo by finding a partner only to see that (deal) collapse still lead this company into the future?
Francioni's term ends after December 2013, and contract extensions for CEOs in Germany are often agreed about a year in advance.
On Thursday, Boerse and NYSE terminated their merger plans after the European Commission blocked the deal to prevent handing the combined group a near monopoly.
Boerse's labour leaders had undermined its campaign to convince German regulators a deal strengthened Frankfurt's role as a financial centre when they urged shareholders to reject the deal, fearing key responsibilities would be moved to New York.
Separately, Deutsche Bank's German retail asset management unit DWS called for a fresh start at the exchange operator in comments published by business weekly WirtschaftsWoche on Saturday.
The merger tied up management capacity for more than a year. In the past couple of years, Boerse has stagnated, and now more dynamism needs to return, said Henning Gebhardt, head of European equities at DWS.
Now and then there needs to be a fresh start - whatever form that might take (...) Francioni, of all people, does not come out of this without a scratch, Gebhardt told the magazine.
The fund manager said he was also unsatisfied with Boerse's development in overseas markets.
Asia is where it's at. That's where to go for a piece of the action. I'm starting to suspect that the Boerse is not always the preferred partner there, he said.
The company must listen more closely to what its customers want, since they are looking for alternatives and are migrating to new platforms like Chi-X or Bats, Gebhardt continued.
Boerse Chairman Manfred Gentz has rejected the idea of any immediate consequences for the Boerse due to the collapse of the NYSE merger, however, calling instead for calm and continuity.
(Reporting by Christiaan Hetzner, additional reporting by Andreas Kroener)
(This story corrects paragraph four to show CEO's contract expires at
the end of 2013, not the end of 2012)