Train from Nice to Monaco during Grand Prix weekend

The train between Nice and Monaco is a regularly scheduled, frequent local train service. Unless things are significantly different during the Grand Prix weekend, there is no way to reserve a particular seat so buying a ticket in advance wouldn't really help. I was there not too long ago and I think I booked the tickets online using the SNCF mobile app. Using that, you arrive at the station and use your booking code at a terminal to get a paper ticket without having to wait in any queues.

See also How to get from Nice to Monaco by public transport? for further ideas on transport from Nice to Monaco.

Regional train tickets are valid on any train of the day when you buy the ticket at the station. You only have to validate it before getting on the train. The price of the ticket does not change over time (I mean booking early does not make it cheaper) and every regional train is the same price.

Therefore I would recommend to just buy a round-trip ticket every day you go there, at the station, and you can come back with any train (of that day, the ticket is only valid on one day). At the station, there are machines to buy tickets that accept coins and credit cards (visas and mastercard most likely but maybe not foreign and other cards). There are tellers but in Nice there is usually a line. So to make sure it works you'd better have coins (one-way is about 4 euros, so you should not have troubles). In case you are late and have no coin, you can still get on a train without a ticket but you should go find the controller and explain that you have no coin and you will pay the ticket price plus 4 euros.

Be careful, still, this applies only to the TER, I.e. the regional trains. This does not apply to TGVs that require a reservation and are usually more expensive.

Saturday will be just fine, but be prepared for Sunday.

Don't need to book a open return. Just mention going to Monaco at the counter. Book a day before or else you will have to get a ticket(which is quick) and queue for the train. The queue moves very slowly as they don't put extra trains for the F1 weekend. Very unlike Silverstone. Trains are packed, so if you want a seat board from St Augustine, many people do. If you are lucky you might get a seat at Nice. After Nice, the trains are jam packed, and be careful about your wallets and valuables. Even if people are dressed like gentleman(woman), be careful. The train driver will anyway remind you through the whole journey. it takes around 20 minutes, so willn't be too taxing on your legs, if you don't get a seat.