The ruling of the Halachic authorities is that you must fast in such a case, as ruled by Maran the Mishnah Berurah (Siman 550, Se’if Katan 12) based on the words of the Ritva, and as ruled by the Maharil Diskin (Kuntres Acharon, Siman 74). However, it should be noted that in certain cases, there is leniency to fast only until midday (Chatzot), following the opinion of the Vilna Gaon (Gra, end of Siman 686) who is lenient in this regard.
Nevertheless, if it were a postponed fast (Tzom Nidcheh), the law would be different, and it would be divided into the laws of the seven days of wedding celebrations (Sheva Brachot) versus the wedding day itself. If a postponed fast falls within the seven days of feasting, according to the Avnei Nezer (Orach Chaim, Siman 427), the groom and bride fast until midday, wait until the time of Mincha Gedolah, pray Mincha including the recitation of ‘Anenu’, and then go to eat and rejoice. This is also the practical Halachic ruling of the Mishnah Berurah (Sha’ar HaTziyun, Siman 559, citing Teshuvot Beit Yehuda) and the author of Yabia Omer (Vol. 1, Siman 34). However, according to Maran the Shevet HaLevi (Vol. 6, Siman 7)—aligning with the Magen Avraham citing the Radbaz, and the Biur Halachah (Siman 549)—one must fast as usual with the rest of the public, even though it is a postponed fast. In practice, we instruct that if the groom feels strong and capable of fasting, he should fast normally. But if he feels weak and it would diminish his joy, we are lenient for him until midday. Regarding the bride, however, we are certainly lenient on a postponed fast, and she does not need to fast at all. Furthermore, on a postponed fast that falls on the wedding day itself, neither the groom nor the bride needs to fast at all.
Yet all of this applies only to a postponed fast; this year, since the fast falls on its originally designated date, both the groom and the bride are obligated to fast.