That part of the law only became effective later, after the “décret d'application” was published (I think it went into effect on January 1, 1994 as provided in the law itself but certainly not before December 30).
But France never had a pure jus soli. What the 1993 law introduced was the need to explicitly request the French nationality. Under the previous law, you would also become French at your eighteenth birthday (and not at birth), but you didn't need to ask for it. So what counts was always the state of the law at the time of your eighteenth birthday.
Even before the change, it was also necessary to be a French resident and to have resided in France during the previous two years to benefit from this particular part of the law. If you were born in France to non-citizen parents who were themselves born abroad but you left the country at an early age, you would not automatically become a French citizen.
After that, the law was amended once more in 1998 to reverse some of the 1993 changes. In the current version, it's not necessary to explicitly request the French nationality anymore (article 21-7 of the code civil). So if you were born in July 1993 and lived in France during your teenage years, you would have turned 18 in 2011 and could have automatically become French, just as it was before 1993.
But that's only the case if you fulfill the residency requirement as well. It is now more stringent than it was before 1993 as you need to have lived in France for five years between your 11th and your 18th birthday (five years from the age of 11 because schooling is mandatory until the age of 16 in France so most people would have no trouble establishing that and it also provides some flexibility; the 1993 version required residency during the five years prior to the application).
There is however another important way to become French that might apply to you, which is called “double droit du sol”. If one of your parents was born in France and you were also born in France, then you are French from birth (this provision is now in article 19-3 of the code civil). This rule is very old and did not change in 1993.