I agree with dt--that Frankie's brother's presence shamed Frankie into realizing that family honor would be destroyed if he testified against Michael. After Frankie recants, Tom tells his brother (in Sicilian): "The honor of the family is intact."

But, as dt said, there are other opinions. One is that Michael was holding threats against Frankie and his brother. Some people here infer that when Frankie told Tom (re. the Romans), "...an' their families were taken care of," that Frankie had family in Sicily who were at risk if he didn't kill himself. Others believe that his brother might have been whacked by Michael.