The distinction is crucial, and constantly misunderstood: winning in Strasbourg does not overturn the French decision. The Court states that the State has violated the Convention; it may order the State to pay compensation; it does not rewrite the judgment.
Bringing a case before it requires having exhausted domestic remedies — in France, up to and including the appeal to the Court of Cassation. It is a narrow door, which opens late, and often years after the events.
The McLibel case ended before it: on 15 February 2005, the Court held that the United Kingdom had violated Article 6 § 1 — because the two defendants, ineligible for legal aid, had had to defend themselves alone against a multinational's lawyers — and Article 10 on freedom of expression.