The European Commission on has released an interesting summary of laws and guidelines: Handbook on addressing the issue of alleged marriages of convenience between EU citizens and non-EU nationals in the context of EU law on free movement of EU citizens
Why might you care, especially if you are happily married to an EU citizen, and definitely not in a marriage of convenience?
Because your right of free movement can only be prevented (except in a few rare cases) if an EU member state has evidence that you are participating in a marriage of convenience (and thus do not have a right of free movement).
The problem is, often staff of the immigration department do not know requirements the law in this area, and reject applications (without regard to the p.26 Burden of Proof) by simply shallowly claiming it is a “marriage of convenience”
Burden of proof is on the national authorities to prove abuse
Married couples cannot be obliged or required, as a rule, to present evidence that their marriage is not abusive.
EU citizens and their family members enjoy the benefit of assumption, meaning that they do not need to provide evidence that their marriage is genuine. To require this would go beyond the requirement to present proof that their marriage is valid.
This reflects the principle of law that the person who lays charges has to prove the charges (‘semper necessitas probandi incumbit ei qui agit‘).
The burden of proof clearly rests on the national authorities who suspect that a non-EU national has entered into a marriage of convenience with an EU citizen for the sole purpose of being granted an EU right to free movement to prove that the marriage is of convenience.