The National Union of Teachers has said it will take up the case of any of its members in this situation after hearing anecdotal evidence that this is happening.
In a briefing note to its local officials, the union said: "Some heads have begun to ask teachers to teach modern foreign languages as part of the primary curriculum, regardless of the teachers' qualifications, skills or experience in the subject."
The union advice said it was reasonable to ask teachers with an A-level in a language to lead lessons in primaries, provided they had additional support. But it added: "The union considers it unreasonable to request a teacher with no or lesser (than A-level) qualifications ... to teach that language."
One teacher wrote to the union to complain after being contacted about the problem by several colleagues in other schools.
The teacher's email reads: "Primary teachers are being ordered to teach French by their headteachers. They are being told that they have to do so for an hour a week, that they will be observed during the year, and that it will be part of their performance management targets.
"They are given no training, no help and may never have learnt French themselves at secondary school. Can you imagine the stress this causes?"
The union has told its members to refuse to take such classes and said it would be prepared to strike over the issue, if necessary.
By 2010, all primary schools are expected to offer language teaching to key stage 2 pupils. Training has been going on in many areas, with primary staff put through intensive courses to brush up their linguistic fluency. But there appear to be few figures on the national take-up of such courses or on the numbers of primary teachers with language GCSEs, A-levels or degrees.
Professor John Howson, director of Education Data Surveys which monitors the schools workforce, said the last government survey of primary teachers' qualifications was in 1988.
"It is quite possible," he said, "that people are being asked to teach languages with little or no training. There is no legal requirement for any teacher to be trained in any particular subject if their school wants them to teach it."
But John Bald, a consultant who leads languages training for primary teachers in Hackney, east London, said: "Most people are giving training priority."