* Second television debate between candidates to lead European Commission
* Candidates agree governments must not override voter choice
* Debate seeks to combat voter apathy, disillusion with EU
FLORENCE, Italy, May 9 (Reuters) - Candidates to lead the European Commission after EU parliamentary elections this month lashed out on Friday against suggestions that the real choice would be made not by voters but by national governments.
The meeting in Florence was the second between the candidates following their first debate in April, part of a broader effort to bring an element of direct democracy to appointing one of the European Union's top officials.
The candidates have been named by the main political blocs in the European Parliament and whichever group secures the largest share of the vote at elections on May 22-25 will be in a good position to put down a marker on the commission presidency.
But a final decision on who will lead the commission - the body that drafts and enforces EU legislation - and succeed outgoing President Jose Manuel Barroso, will be made by EU leaders and confirmed by the European Parliament.
Suggestions that the result of the vote would be set aside by national governments drew a fierce reaction from the candidates, who argued that it would be a setback to European democracy at a time of growing voter disillusion.
"If they did that I would be very angry," said Jean-Claude Juncker, the former Luxembourg prime minister who is the candidate for the centre-right.
"They would be opening the way to a major crisis between the European Parliament and European governments and by the way they would be telling European voters their vote does not count."
There were clear differences on important issues, including whether or not member states could be allowed extra flexibility on meeting budget targets with centre-left candidate Martin Schulz in favour and both Juncker and Guy Verhofstadt, the candidate from the liberal bloc, against.
But all three, as well as Jose Bove, the French environmentalist campaigner who is one of the two Green Party candidates, agreed that the Commission had to resist being sidelined by powerful national governments.
"If you have to ask for a green light from Berlin and Paris, you eliminate a driving force of European integration," Verhofstadt, a former prime minister of Belgium, said.
It remains unclear what impact a campaign around a contest for the Commission head will have on voters, many of whom are deeply disillusioned after a five-year-long economic crisis that is only starting to show signs of easing.
Only the moustachioed Bove, who made his name with a fiery campaign against international chains such McDonald's restaurants, has much of a public profile outside their home countries or the corridors of Brussels where most have spent much of their careers.
The election, the first since the euro zone debt crisis of 2011 threatened to destroy the single European currency, has been marked by the rise of anti-system parties such as the 5-Star Movement in Italy, the National Front in France, or UKIP in Britain, as well as the prospect of high voter abstentions.
(Editing by Jason Neely)