Hello Estraine and thanks for your translation.
You invite us to correct. Here are my suggestions:
et nous courrions vers elle > and we (walked) would run toward it
Et puis nous marchions sur la plage > And (than we went) then we walked on the beach
les mettant à ton oreille > (held) putting them at your ear
je me rappelle > (I remember me) I recall
Tu avais toujours si faim > You (have always been) were always so hungry
je me souviens > (I remember me) I remember
et nous étions bien > and we (had been) were well
Et c'est toujours lui le soleil > And (it was always it) he is always the sun
et l'enfant aux cheveux blonds > and the blond (children) child
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Good luck!
Please help me with grammar faults.