There's no single answer to this question! It depends on the destination, the potential difficulty of the route, the logistics involved, and much more. In some cases, going solo and unsupported is a perfectly realistic option — in others, it's a real risk that could lead to serious trouble. Here's a look at the key factors that will help you answer this question before heading out on a trek.
Going trekking: the influence of your destination
Your destination and choice of trek route is the first factor that will influence whether you organise the trip yourself or go through an agency. It's fairly straightforward to plan and successfully complete your own trek in France and in many European countries (not all). You'll find plenty of information from hiking federations and various associations. There's also an abundance of literature and trail guides, often very well put together. You'll be in countries with broadly similar legislation to France, or with comparable rescue services. And finally — particularly in France and some neighbouring countries — the language barrier is not a major obstacle.
On other continents, however, you may encounter specific legislation (some countries, for example, require trekkers to go through agencies). You may also find different rescue infrastructure or access conditions. The language barrier can be a real communication problem. And some regions present their own specific challenges — climate, access, general safety — that may make the support of an agency necessary.
These rules are not set in stone. There are treks in France that are better done with company, and others in remote corners of the world that you can organise independently. Each situation requires careful consideration — try to gather as much information as possible before making your choice.
Logistics
Going fully self-sufficient on a trek is a personal choice. But depending on the type of route, you may need to carry equipment, arrange bivvies, and manage your food supply according to how remote the areas you're crossing are. This can also tip the balance. The heavier the logistics, the more an agency can add value — helping plan resupply points or organise specific transfers.

Your experience
Your experience is of course a key factor when deciding between booking with an agency or going it alone. If you've never organised a trek before, it's best not to head straight into exotic terrain on the other side of the world.
It goes without saying that it's better to build up experience in areas where you feel more confident. Start, for example, by organising your own treks in France — particularly in mountain ranges or regions you know well.
The skills required to go trekking entirely under your own organisation fall into two main categories. First, there's your physical fitness and your experience of this type of route. Then there are your technical abilities: organisation and preparation, map reading and navigation, cooking for yourself at a bivvy, and being comfortable in English or the local language.

Going trekking: the social side of adventure
Organising a trek yourself has its appeal, but you'll most likely be doing it with family, a group of friends, or on your own. Agency-organised trips offer the chance to meet new people and learn something about yourself and others. This factor depends entirely on your personality and whether or not you want to mix with other people.

Don't underestimate the time it takes to organise a trek. It's proportional to the duration and difficulty, of course, but it's a genuinely time-consuming task that usually needs to be started months in advance. Agencies offer the freedom of turning up with just your pack and boots, ready to go. Today there are also hybrid formats — "freedom trips" where the agency handles the essentials but gives you the autonomy to hike on your own. These are a good compromise for those who want to avoid the full group-tour experience. Make your choice based on these factors — but above all, remember that going trekking should remain a pleasure and should never come at the cost of your safety!