Azure Language Detection is part of Azure AI Language Services. Yes, there is a free tier for language services.
See the following statement from the language service page.
Summarization, sentiment analysis, key phrase extraction, language detection, question answering, named entity recognition, and conversational language understanding all share 5,000 free text records per month.
After the free tier, the standard tier applies, where you can find the pricing in the below link.
Refer: https://azure.microsoft.com/en-us/pricing/details/cognitive-services/language-service/
The pricing is per thousand text records (Text Records correspond to the number of 1,000-character units.). So the unit rate reduces as your consumption increases.