Hang a string of lights between two hooks and it sags. That sag is the whole charm, and it is also why a string that matches your balcony's width on paper turns out short. A 3 m gap with a 30 cm dip needs about 3.1 m of string. Add a lead cable to the socket and a bit of slack at each hook, and the "3 m" set you nearly bought is already too small.
The planner below does the sums for you. Set your width, choose how many swags (the scallops between hooks), and drag the dot to set how deep they hang.
Set the width to 300 cm with a 30 cm dip. One swag needs about 3.1 m. Split the same gap into four swags with the same 30 cm dip and the total jumps to about 4 m, because each short swag still has to dip just as deeply. The dip matters more than the width of each scallop, so if you want lots of gentle scallops, shrink the dip with them.
A relaxed look tends to come from a dip of roughly a tenth of the swag's span; much deeper than a quarter of the span starts to look droopy. These are matters of taste, so drag the dot and trust your eye.
String lights are for mood, not for seeing by. Pick warm white, around 2200–2700 K, the same cosy range as a lamp in the living room, and keep the bulbs dim. A few small bulbs at 30–50 cm spacing glow softly. Dense, bright strings at eye level start to glare and, after dark, can shine into your neighbours' windows too.
Cosy does not need more. If you already have a string that's slightly too long, loop the extra over a hook or add a swag. A little extra length can be pleasantly slack, whereas a string that is too short cannot be fixed.
A tiny balcony may only need one short, shallow swag across the door frame. A pergola or long terrace may suit a zig-zag overhead rather than scallops along one edge, which needs more string and more hooks. Use the planner as a starting point, then adjust to the space.