It didn't last long enough for me to make out the language. I thought latin at first but one of Claudia's lines sounded oddly spanish. Perhaps this was just badly pronounced latin.

The "magic formula" the mother muttered over the cup of wine later on was definitely in latin.

Claudia didn't look Roman at all, though, and from the way she named her son (one name, and an israelite one), she wasn't.

It looks like the women used latin as a lingua franca, much like they conventionally switched to the modern lingua franca with different accents once that was established.

The game found on the beach was based on a Babylonian design, I think.