@messicano
According to the
GSM Association there're only two GSM networks in Mexico, TELCEL and MOVISTAR. Both are running on GSM1900, whereas European GSM networks operate at 900 and 1800 MHz.
So the very first question is, is your Mexican SIM-card and phone from one of the named operators? If not you're likely to be a customer of a IDEN- or CDMA-network, which are both standards incompatible with European GSM-networks. (However CDMA phones doesn't have SIM-cards, do they?)
The next question is, what frequencies do your phones support? To answer this question we need the exact designation of the phone models. If you don't have at least a triband or better quadband phone, which means the phone would support 3 or 4 of the GSM bands at 850, 900, 1800 and 1900 MHz, the phones won't work on the other continent.