French language Q&A Forum

Do non-reflexive verbs used in the past tense with a reflexive pronoun use être or avoir?

For example, if the above sentence "Les deux chiens se fixèrent avec méfiance" is put in the past tense, do we use être with the verb "fixer" (-->"Les deux chiens se sont fixées avec méfiance")?

Or, am I asking the wrong question? In other words, in French perhaps there is no such thing as verbs that are "non-reflexive." Instead, is it that case that any verb used with a reflexive pronoun automatically becomes a reflexive verb, which means the rule regarding use of être in forming the past tense applies?