The unlikely imposter
The fact that an imposter might come along and steal a life from someone is ironic. The fact that she believes him is even more ironic.
The irony of memory
Another necessary component of this ironic story is that memory actually doesn't do the thing we believe it does. The memory rationalizes the present to a list of experiences in the past, but when we believe we will be happier with a lie, the mind can choose to misremember for the purposes of a happier existence. So the memory is subjective and often not trustworthy. The idea that one should distrust even their own memories is a great irony.
The irony of marriage
Marriage is ironic. If the imposter had thought more clearly about what marriage was really like, maybe he would have been less kind to his alleged wife than he really was. But, the imposter only has his best guess about their marriage, and it would make sense that marriage would be romantic and service-oriented. That's not what real marriage is like, 9 times out of 10. Therefore, marriage itself is an ironic aspect of the novel.
The irony of abuse
By treating someone else like an object, as Martin Guerre does to his wife, he brings more suffering upon himself. The wife is the more obvious character for pity, but look closer at Martin. His mistreatment of his wife makes her willing to settle for a fake. The emotional damage of that realization, as well as the dissolution of his marriage, are Martin's price to pay for that mistake, in a way. This means that by seeking to control his marriage, he destroyed it.
The irony of the subjectivity
The core irony of subjectivity is that not only do we see things from points of view, we're often not even honest with ourselves about our points of view, which makes things even more subjective, because we're willing and able to fashion our lives around convenient lies, instead of difficult truths. Therefore, we're subject to ourselves in an even greater way than classical subjectivity. We're subject to our own dishonesty and willingness to be misled.
