Some, not all european languages are derived from Latin. Most European, Indian, Central Asian and Iranian languages today form a family of languages called Indo-European.
What are the modern Indo-European languages spoken today?
Many! Indo-European family is the largest family of languages. It can be divided into different groups.
Indo-Iranian: Hindi, Oriya, Bengali, Marathi, Sindhi...., derived from Prakrits and eventually old Sanskrit as well as Iranian languages such as Pashto, Farsi, Dari...
Balto-Slavic: Russian, Bulgarian, Polish, ... and Estonian, Latvian,...
Romance: French, Italian, Romanian, Spanish,... all the languages descended from Latin.
Germanic: English, German, Swedish, Icelandic, ...
Greek
Albanian
and so on.....
Did all the Indo European languages originate from Sanskrit?
Not at all! Sanskrit is merely the oldest of the known classical Indo-European languages. That is all.
All the Indo-European languages have a common ancestry, namely a very old language called Proto-Indo-European (abbreviated PIE) which is far older than Sanskrit. To say that these languages originated from Sanskrit is totally incorrect. The popular notion in India (that Sanskrit is the 'mother of European languages') is completely wrong. It owes its origin to the completely outdated thesis of Max Mueller.
Proto-Indo-European (PIE) was probably spoken in a region around Iran. Some Eurocentric philologists place the source of PIE at the steppes of Russia and elsewhere closer to Europe. But I have reason to believe that they are wrong.
Sanskrit is a descendent of PIE, just like Latin, Greek, Avestan or Celtic.
What are the other language families?
Dravidian: Tamil, Telugu, Kannada, Brahui (Pakistan), Malayalam.
Hamito-Semitic: Arabic, Hebrew, Coptic (?), ...
Nilo-Saharan: Swahili, Hausa, Ibo,...
Mon-Khmer: Cambodian, Thai, Malay,...
Sino-Tibetan: Chinese, Burmese, Tibetan, Cantonese, Mongolian...
Finno-Ugrik: Turkish, Hungarian, ...
How are Dravidian and Indo-European languages related?
If you go further back in history (say, 10,000 BC or more), the Dravidian and Indo-European languages are cousins. Both these language families, and a few others such as Hamito-Semitic, Kartvelian, Finno-Ugrik and a few other languages are descended form a very very very ancient language called Nostratic.
What are the Nostratic languages?
All languages that are descended from this very very very ancient language Nostratic are called the Nostratic languages. They all belong to the Nostratic super-family.
Examples of Nostratic languages: Hindi, English, Oriya, Turkish, Farsi, Russian, Arabic, Tamil, Kannada, Hungarian, Hebrew.....
(These languages are spoken by people of the 'caucasoid race')
Examples of non-Nostratic languages: Thai, Chinese, Swahili, Hausa, Santali, Vietnamese, Malay, Quechua, Inuit, ....

