There is no known benefit of a gluten-free diet on fertility unless you are diagnosed with celiac disease or sensitivity to gluten.

Celiac disease is an immune reaction to eating gluten. You can find it mostly in wheat, barley and rye. If you have celiac disease, eating gluten triggers an immune response in your small intestine. The only known treatment for it is the elimination of trigger foods and beverages.

On the gluten-free diet, you can have foods that are naturally without gluten or you can also eat substituted foods like bread from flours of rice, buckwheat, corn, brown rice, amaranth, quinoa, or millet.

Celiac disease may be a reason for some alterations in male and female fertility. Check from the symptoms below:

Female fertility	Delayed onset of menses, no periods, early menopause, recurrent miscarriages, reduced rates of pregnancy, unexplained infertility
Male fertility	Testicular dysfunction, altered sperm morphology and motility, and reduced sexual activity
Alterations in pregnancy	Repeated miscarriages, premature delivery, impaired fetal growth, abnormal placental function, pregnancy anaemia

If you have any of the above issues, and no diagnosis, there may be a value of getting tested for celiac disease.

In case you are gluten sensitive, start gluten-free foods as soon as possible. Avoiding gluten seems to lengthen the fertile life span in celiac women. It has been shown to improve fertility and reduce the risk of further reproductive problems.