Any suggestions for Day Use offices in Paris, Florence or Rome?

Practically all 4 star hotels will have business centers and conference rooms available. The other option is to kick the family out and send them visiting places while he takes the business calls from the room. Unless you stay at a cheap hotel, any hotel that caters to business travelers will have adequate space and wifi speed to take a call on skype. Wifi speed is on average higher and cheaper in Italy, therefore if you stay at a business hotel you'll have faster service than at home. But if you stay at a budget 2 star bread and breakfast, that may not be the case.
The standard base for Internet speed in Italy, for example with Telecom Italia, is 7Mbps, but if you want the next level, it's as high as 10Mbps. They even have the option at 30Mbps (called Telecom Tuttofibra) or 100Mbps (called Tuttofibra plus), speeds unheard of in the U.S.
In the US even the highest tier with AT&T U-verse is 6Mbps.

Where are you staying? The really excellent hotels in France and Italy always include business center where he could use the desks/workspace and high speed internet connections with no need to pay for an office in some other building.

Try Regus business centers.

Going to the trouble of renting an office from Regus (not available in Florence) or similar outfit for just taking a conference call makes no sense whatsoever. With the money you'd spend to rent it you could upgrade to a mini suite in a business hotel.

My husband regularly works when we're on vacation. When the kids were younger, he'd leave the hotel room and find a quiet location behind the hotel or near a closed pool in the evening (Jamaica and Florida). Now that they're older, he goes back to the hotel while we explore the city or he finds a quiet place in a park or such area near where we are exploring and he does the conference call there. If its in the evenings or when we're around we either tell the kids to be quiet (which they do) or we leave for a bit. In London he was fortunate as his business has an office there that he went and worked out of for a few days but I can't imagine renting office space for him. I'm sure the hotel would have a place he could go if none of the other options work.

Thank you!