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You are free to search for a job in the Middle East on a tourist non-employment visa.
However, you cannot be employed on that visa. This is highly illegal and there are serious repercussions for both you and your employer.
If you are on a visit visa and you happen to be offered employment, you have to leave the country and come back on a suitable visa in order for you to legally work.
The type of visa you will need will depend on your employer (if its government, private sector, or under a government contract to a private sector company) and how you are hired (directly, contract, though a government manpower agency, etc).
For schengen countries, the policy varies per member state. Generally speaking, only Annex II state citizens are allowed to work during their visa-free stay. However, beyond that stay, they are also required to obtain the correct visa.
India is an Annex I state, which means unfortunately this does not apply to you.
However for seeking employment there are no specific restrictions that I have been able to find.
The wikipedia listing on the visa policy of the schengen area has some excellent information in this regard.
However in all cases you cannot be permanently employed unless you are admitted into the country on a visa that indicates your eligibility for employment in the country; and to do this you will have to exit and re-enter.