I have played all the games below with children of that age at parties, either in school or at church parties.
To start as the children arrive:
Have some music playing, blow up balloons and leave them in the room. Just let children play with them - hitting them in the air, dancing with them, kicking them.... as long as they don't hit each other, that's fine.
A good first game:
Stick small round stickers all around the room, at child height, some more visible than others. Allow at least 10 per child (and have some spare to add later). Give each child a piece of card with their name on it. Tell them to hunt the stickers and stick them on the card. (The spare stickers are for if there's a child who hasn't found many, so you can 'plant' some extra). If you want, you can give a prize for the child whose won the most.
Some active games (these need a fair bit of room):
Musical animals - Play music, tell the children to move around the room like an animal. Each time the music stops, the children have to freeze, and then you change the animal. Kind of like musical statues, but no-one goes out (you could give a prize to the best animal imitation of each round I suppose), and you don't have the difficulty of that child who won't dance or just shuffles their feet!
Game of four corners - Stick pictures around the room (if you're doing a theme party, this could tie in with your theme, if not, animals colours, numbers, whatever you fancy). Children run around the room (to music if you wish). When the music stops, call out one of the pictures and the children have to run to it. I used to use this game to teach numbers or foreign languages, it works well with children without much English because they can follow the crowd.
Beep-beep game - Give each child a round item (e.g. a plastic plate) to use as a steering wheel. They have to run around the room. Each time they come near another child they have to shout 'beep beep' and steer away. Every so often you can tell them all to change direction.
Bean game - Children are 'beans'. When you shout 'jumping beans' they have to jump up and down on the spot. 'Runner beans' = run around. 'Jelly beans' = stand still and 'wobble' all over. ' 'Baked beans' = lie flat on floor. etc. Try here
for more ideas. Be warned, the leader needs to be very fit in this game!
Sock game - Divide room in two (e.g. with a line of chairs). Put children in teams. In each section, empty a bag of balled up socks (clean). On a signal, children have to throw as many socks as they can into the opponents area. They have to stop on the second signal. Count the socks. Whoever has the least, wins. Wash the socks!
Some quiet games:
Card puzzles - Cut up old birthday cards to make simple jigsaw puzzles (or pictures related to a theme). Put one piece of each puzzle on a table, spread the rest out on the floor, face up. Give each child one of the puzzle pieces from the table. They have to complete their puzzle (they will need a place to do this). When they have done so, they come back to get another puzzle piece from the table. And so on, until all puzzles are completed.
Bring me (Chinese market) - Sit children in teams, each with an adult. One adult sits in centre of teams. This adult then says 'Bring me xxx.' One child from each team then has to bring them the required item. First team to do so wins. The items could either be something that could be found in the room, or you can give children pictures (birthday cards again) that have been sorted out beforehand and ask them to bring you a picture with xxx on it (e.g. Bring me a card with a candle on it). The adult with each team needs to ensure each child has a fare share of turns at bringing items.
Sleeping Lions - Get children to lie down on the floor. They have to lie as still as they can. If they move... they're out!
What’s changed? Take a child out of room, & change something about their appearance. Rest of the group have to say what has changed.
The next three games are good to help you (and the other children) learn names...
Jelly Game – Sit in a circle. Leader throws ‘jelly’ at a child, saying their name. The child then pretends to scrape it off their face, and throws to another child. Last child has to ‘eat’ the jelly… then gets told (by the leader) what flavour it was.
Good morning your majesty – Sit one child on a ‘throne’ in centre of circle, blindfolded. Choose another child to come & say ‘Good morning your majesty’. King / queen has to guess who it was.
Who is missing? – sit in circle, one child is blindfolded. Send another child to hide. Blindfolded child has to say who is missing.
I hope that helps. If you decide to do a theme party I might have other ideas...
P.s. I see you're in Morges, which is near me. I have a (small) parachute hanging around somewhere. Parachute games are great fun, if you have enough space, and can be used outside or inside (you just do different games). I've used my parachute with up to 15 small children. If you'd like to borrow it, you'd be welcome.