Mr Vaz told BBC Radio 4's Today programme that: "It was clear that the French wanted to put tax and social security on the agenda."
The paper claims that the UK will be unable to block the directive which would force companies to consult workers on redundancies and bring in new rules on the sale of subsidiaries as, it says, Germany now backs the proposal.
But on the day after Vauxhall announced the end of car production at its Luton plant, Mr Vaz said the government did not support the proposal.
"There needs to be a lot of improvement in the text of this. We do not support the way in which it is proceeding.
"As this is the only newspaper that reports Mr Schroeder's [the German chancellor] alleged views I think we can take this as not being the German position."
The move, which could force the government to take sanctions against companies which ignore the directive, he said, had not been on the agenda during the weekend's EU summit in Nice as "there was not enough support".
Veto lines will not be crossed
The Foreign Office minister then turned to the fallout from the summit and remarks from the head of the EU Commission, Romano Prodi.
Mr Prodi said he regretted the decision of some member states, most notably the UK, not to surrender the national veto on tax and social security issues.
Mr Vaz told BBC Radio 4's Today programme that: "It was clear that the French wanted to put tax and social security on the agenda."
But he re-stated the government's position that: "We are not going to accept qualified majority voting on tax and social security."
He added: "This is set in stone and crystal clear."
But one of the UK's two EU commissioners, the former Labour leader, Neil Kinnock, said on the same programme that the deal reached at Nice was simply part of the "evolving development" of the EU.
Looking ahead Mr Kinnock strongly hinted that within a few years there would have to be further reform of the national veto.
Prodi's 'disappointment'
Mr Kinnock also sought to downplay the remarks made by Mr Prodi in Strasbourg on Tuesday which had been interpreted as an indirect attack on the UK's position at the summit.
"What President Prodi actually said in the European Parliament was a generalised statement about his disappointment at the outcome of the summit."
"As with all European councils, what we saw as the outcome at Nice was as far as the council of the heads of governments of the member states are prepared to go at the moment.
'Evolving Union'
"This is an evolving development in the European Union.
"Whilst there will be some, including Romano Prodi, who wanted further progress there are others who will say this was about right in terms of perceptions of the next four, five, six years of the European Union," he said.
Mr Kinnock's remarks are likely to be seized on by Conservatives who have claimed that the Nice agreement was another step on the road to a European superstate.
They believe that Britain will face increasing pressure to give up national vetoes in vital areas.