This is a very interesting question to consider. I would argue that the chief archetype that links both of these excellent texts involves the archetype of the journey. However, in the case of these texts, the journey is not a literal archetypal journey as in The Odyssey, but a metaphorical journey towards self-identity and self-knowledge. In a sense, both Jane Eyre and Oedipus Rex feature the struggle of the central character to identify themselves and discover who they really are. Jane has to struggle to balance the two opposite compulsions of "feeling without judgement" and "judgement without feeling," as expressed by the two characters Bertha Mason and Helen Burns. At the end of the story, however, she is able to hold these two extremes in tension and can live a happy life, secure in herself and in her identity.
Oedipus, however, has often been viewed as a detective who doesn't know that the person he is so desperately trying to track down is actually himself. As the play progresses, he moves ever onwards towards self-discovery as he realises his own identity and the tragic fate that has befallen him. Both texts therefore seem to adapt the archetype of the journey with very different impacts.