Mona visite à Boulogne

"visite" is feminine => ma

Reécemment, je suis allé à Boulogne pour me reposer dans le nNord due la France.

"France" is a feminine country
Cardinal points are capitalized when they correspond to something specific culturally or socially: this is typically the case of "le Nord de la France", which is not just Northern France but a region imbued by a typical ch'ti culture

J’ai visité une belle cathédrale et m’aie suis promené dans la vieille anciennville.

"se promener", like all reflexive verbs, require the auxiliary "être" => je ME SUIS promené
The old part of French towns is typically called "la vieille ville"

Moi et ma famille nous relaxionet moi nous sommes relaxés/détendus ensemble à la plage, malgré les vents forts.

It's a customary politeness rule to quote the "moi" element last in a enumeration => ma famille et moi

Main action of the narrative = passé composé => nous nous sommes relaxés

"vent" is mostly pluralized in seafaring or weather forecast contexts, where there can indeed be several types of wind, so several "vents"
I'd use the singular here
"malgré les bourrasques" would also be right

Notre visite n’était'a duré que 'une journée, puisque nous adevions besoin de retourner enrentrer/repartir le soir, mais lae voyage était passionnant.

durer = to last (this verb is much more used than its English equivalent)

"avoir besoin" in French is used for things you actually need; it's not really a synonym of "to must/to have to"

to depart (after arriving) = repartir
"rentrer" would be alright though