nous évitera

Patricia, 

this is a pretty complex sentence in French (especially at B1 level, I think ).

The ‘simple’ answer to your question is that it is the infinitive ‘ marcher ‘, used as a noun, that is the subject of éviter in this sentence. 

 ‘ Nous ‘ (preceding éviter) is an indirect object , and cannot be replaced by the subject pronoun ‘ on ‘.

When used as nouns, infinitives follow 3rd person singular conjugations, giving the future tense of the verb éviter as ‘évitera’ in the sentence.

The sentence is complex because there are 2 verbal expressions following the subject, the latter including a pronominal verb : 

1. “ éviter à qqn de faire qqc “ ( à qqn giving rise to the indirect object pronoun ‘ nous ‘  in this sentence, which cannot be replaced with the subject pronoun ‘ on ‘ ) 

and with ‘ faire qqc ‘ replaced by 

2. ‘ se tromper de qqc ‘ ( another fixed expression )

 https://progress.lawlessfrench.com/revision/glossary/verbal/infinitif-infinitive 

https://www.thoughtco.com/french-infinitive-linfinitif-1368866 

https://www.lawlessfrench.com/grammar/infinitive/

https://www.wordreference.com/fren/%C3%A9viter 

 https://www.wordreference.com/fren/se%20tromper%20de