Je pense que c'est un montant fixe soustrait du montant de la compensation éventuelle, comme lors d'un accident par exemple, que l'assurance compense moins une franchise donnée.

I'm not sure there's an exact translation for this. "Franchise" is being used here in the way "deductible" is used in insurance claims, for example. Here, the client can expect no adjustment to the rent unless the difference -- in either direction -- is greater than 1.5% of the total area expected. I think measurement delta conveys the meaning accurately.
You could also try wording it with cap, in the sense that the part the client will have to take at his or her charge is capped at +/- 1.5% of the expected measured area.

I'm reading the ST as saying that "qui" in qui constitue une franchise refers back to pourcentage de tolérance visé . That phrase pourcentage de tolérance visé might be called an "error margin" (or "margin for error" (although it's actually called a "tolerance" in the ST).
The ST, where it refers to franchise" is focused on the difference in floor area that exceeds the "error margin / margin of error".

IOW, there's no justification for a claim unless the actual (measured) error exceeds the "(allowable) margin of error" defined in the contract.

Of course, a franchise (like a margin) covers a range of actual values from below to above zero (more floorspace or less floorspace than expected).

Définition de la franchise d'impôt (partial tax exemption)

La franchise d'impôt désigne le fait pour un contribuable, pouvant être une personne physique ou une entreprise, de bénéficier d'un certain plafond en dessous duquel une somme d'argent normalement soumise à un impôt en sera exonérée. Des franchises d'impôts peuvent exister pour certaines entreprises installées dans des zones sensibles. De même, des franchises d'impôt peuvent être envisagées en matière de donation, comme c'est habituellement le cas en France lorsque le montant de la donation ne dépasse pas un certain seuil.

The concept of ‘franchise d’impôt’ can clarify the concept of ‘franchise’ in the TXT if you replace ‘une somme d’argent’ with ‘floor area correction’ and ‘impôt’ with ‘rent decrease/increase’.

Proof: If the floor area correction is negative (the floor area was overestimated) and equal to 1.5% of the initial floor area or less, then there is neither a rent increase nor a rent decrease.

However, if the same, negative floor area correction is greater than 1.5% of the initial floor area, then there is a RENT DECREASE.

By the same token, if the floor area correction is positive (the floor area was underestimated) and equal to 1.5% of the initial floor area or less, then there is neither a rent increase nor a rent decrease.

However, if the same, positive floor area correction is greater than 1.5% of the initial floor area, then there is a RENT INCREASE.