Well, I suppose that you know that a VEFA contract "Vente en l’état futur d’achèvement, entails buying what is usually an appartment before the building is built.

And I suppose that you also know that "régulariser" is most often used with regard to enablling illegal immigrants to "straigten out" their illegal status.

In the context of your text, I would say...

Consequently, he expressly |demands / requires] that the undersigned notary, Maïtre +++++, [properly] formalise this sale.

OR that Maïtre +++++, the undersigned notary...

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Termium gives ...

Français :Traduction

officialiser s

Anglais :Traduction

formalize s VERBE

régulariser s
donner un caractère officiel s
donner un caractère définitif s
donner une forme officielle s
donner une forme définitive s
adopter formellement s
adopter officielle

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Having said that, you could also say...

properly register
properly conslude
properly record

OR even

put this sale right [in accordance with applicable law].