Sven,
a truly free electron cannot interact with a photon in a sense that it would absorb it, or otherwise gain net energy from it.
This is because energy and momentum cannot be simultaneously conserved in such an interaction.
Compton scattering takes place with the electrons interacting with the material and each other, this makes it possible for the surrounding particles to absorb/supply energy and momentum through em interaction, this makes photon-electron interaction possible. In other words, the electrons are not completely free.
You see, details make a big difference, there is no "one answer fits all" to your question, it depends on what it is you have in mind exactly.
When seen as an EM wave, the EM fields would interact with the free electron, but there cannot be any net energy transfer, but if the frequencies are low and the electrons are not "free electrons in vacuum" but "free electrons in a material", energy can be transformed to heat..
To get a real answer, you must have a real question related to a real experiment, so you can figure out which effects are possible or impossible and which effects are relevant or irrelevant.
Forced vibrations in EM-wave? What will happen?
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